Device and method of improving the perceptual luminance nonlinearity-based image data exchange across different display capabilities

ABSTRACT

A handheld imaging device has a data receiver that is configured to receive reference encoded image data. The data includes reference code values, which are encoded by an external coding system. The reference code values represent reference gray levels, which are being selected using a reference grayscale display function that is based on perceptual non-linearity of human vision adapted at different light levels to spatial frequencies. The imaging device also has a data converter that is configured to access a code mapping between the reference code values and device-specific code values of the imaging device. The device-specific code values are configured to produce gray levels that are specific to the imaging device. Based on the code mapping the data converter is configured to transcode the reference encoded image data into device-specific image data, which is encoded with the device-specific code values.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationNo. 61/567,579 filed 6 Dec. 2011; U.S. Provisional Patent ApplicationNo. 61/674,503 filed 23 Jul. 2012; and U.S. Provisional PatentApplication No. 61/703,449 filed 20 Sep. 2012, all hereby incorporatedby reference in entirety for all purposes.

TECHNOLOGY OF THE INVENTION

The present invention relates generally to image data. Moreparticularly, an embodiment of the present invention relates toperceptual nonlinearity-based image data exchange across differentdisplay capabilities.

BACKGROUND OF THE INVENTION

Advances in technology allow modern display designs to render image andvideo content with significant improvements in various qualitycharacteristics over the same content, as rendered on less moderndisplays. For example, some more modern displays are capable ofrendering content with a dynamic range (DR) that is higher than thestandard dynamic range (SDR) of conventional or standard displays.

For example, some modern liquid crystal displays (LCDs) have a lightunit (a backlight unit, a side light unit, etc.) that provides a lightfield in which individual portions may be modulated separately frommodulation of the liquid crystal alignment states of the active LCDelements. This dual modulation approach is extensible (e.g., toN-modulation layers wherein N comprises an integer greater than two),such as with controllable intervening layers (e.g., multiple layers ofindividually controllable LCD layers) in an electro-opticalconfiguration of a display.

In contrast, some existing displays have a significantly narrowerdynamic range (DR) than high dynamic range (HDR). Mobile devices,computer pads, game devices, television (TV) and computer monitorapparatus that use typical cathode ray tube (CRT), liquid crystaldisplay (LCD) with constant fluorescent white back lighting or plasmascreen technology may be constrained in their DR rendering capability toapproximately three orders of magnitude. Such existing displays thustypify a standard dynamic range (SDR), sometimes also referred to as“‘low’ dynamic range” or “LDR,” in relation to HDR.

Images captured by HDR cameras may have a scene-referred HDR that issignificantly greater than dynamic ranges of most if not all displaydevices. Scene-referred HDR images may comprise large amounts of data,and may be converted into post-production formats (e.g., HDMI videosignals with 8 bit RGB, YCbCr, or deep color options; 1.5 Gbps SDI videosignals with a 10 bit 4:2:2 sampling rate; 3 Gbps SDI with a 12 bit4:4:4 or 10 bit 4:2:2 sampling rate; and other video or image formats)for facilitating transmission and storage. Post-production images maycomprise a much smaller dynamic range than that of scene-referred HDRimages. Furthermore, as images are delivered to end users' displaydevices for rendering, device-specific and/or manufacturer-specificimage transformations occur along the way, causing large amounts ofvisually noticeable errors in rendered images in comparison with theoriginal scene-referred HDR images.

The approaches described in this section are approaches that could bepursued, but not necessarily approaches that have been previouslyconceived or pursued. Therefore, unless otherwise indicated, it shouldnot be assumed that any of the approaches described in this sectionqualify as prior art merely by virtue of their inclusion in thissection. Similarly, issues identified with respect to one or moreapproaches should not assume to have been recognized in any prior art onthe basis of this section, unless otherwise indicated.

GB 2311432 A discloses a method for converting an input frame of imagedata into a plurality of output frames of different spatial frequencyspectra. After applying an individual gain to each output frameaccording to a model of the human visual system, the output frames arecombined, thereby sharpening or softening the input image.

US 2003/0174284 A1 discloses a contrast sensitivity test embodied as atwo-alternative forced choice examination using grating stimuli ofrandomly interleaved spatial frequencies.

WO 2007/014681 A1 discloses a method for calibrating a display systemsuch that the display system conforms to an enforced standard for aselected range of parameters. Images encoded according to a standardizedgreyscale standard display function are converted into display-specificdigital driving levels. The digital driving levels are converted intoluminance output according to a native transfer curve of the displaysystem based on human contrast sensitivity.

SUMMARY OF THE INVENTION

-   -   The invention is defined by the independent claims. The        dependent claims concern optional features of some embodiments        of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example, and not by wayof limitation, in the figures of the accompanying drawings and in whichLike reference numerals refer to similar elements and in which:

FIG. 1 illustrates an example family of contrast sensitivity functioncurves that span across a plurality of light adaptation levels,according to an example embodiment of the present invention;

FIG. 2 illustrates an example integration path, according to an exampleembodiment of the present invention;

FIG. 3 illustrates an example gray scale display function, in accordancewith an example embodiment of the present invention;

FIG. 4 illustrates a curve depicting Weber fractions, according to anexample embodiment of the present invention;

FIG. 5 illustrates an example framework of exchange image data withdevices of different GSDFs, according to an example embodiment of thepresent invention;

FIG. 6 illustrates an example conversion unit, according to an exampleembodiment of the present invention;

FIG. 7 illustrate an example SDR display, according to an exampleembodiment of the present invention;

FIG. 8A and FIG. 8B illustrate example process flows, according to anexample embodiment of the present invention;

FIG. 9 illustrates an example hardware platform on which a computer or acomputing device as described herein may be implemented, according anexample embodiment of the present invention;

FIG. 10A illustrates maximums for code errors in units of JNDs in aplurality of code spaces each with a different one of one of one or moredifferent bit lengths, according to some example embodiments;

FIG. 10B through FIG. 10E illustrate distributions of code errors,according to some example embodiments; and

FIG. 11 illustrates values of parameters in a functional model,according to an example embodiment.

DESCRIPTION OF EXAMPLE EMBODIMENTS

Example embodiments, which relate to perceptual luminancenonlinearity-based image data exchange across displays of differentcapabilities, are described herein. In the following description, forthe purposes of explanation, numerous specific details are set forth inorder to provide a thorough understanding of the present invention. Itwill be apparent, however, that the present invention may be practicedwithout these specific details. In other instances, well-knownstructures and devices are not described in exhaustive detail, in orderto avoid unnecessarily occluding, obscuring, or obfuscating the presentinvention.

Example embodiments are described herein according to the followingoutline:

-   -   1. GENERAL OVERVIEW    -   2. CONTRAST SENSITIVITY FUNCTION (CSF) MODEL    -   3. PERCEPTUAL NONLINEARITY    -   4. DIGITAL CODE VALUES AND GRAY LEVELS    -   5. MODEL PARAMETERS    -   6. VARIABLE SPATIAL FREQUENCIES    -   7. FUNCTIONAL MODELS    -   8. EXCHANGE IMAGE DATA BASED ON REFERENCE GSDF    -   9. CONVERTING REFERENCE ENCODED IMAGE DATA    -   10. EXAMPLE PROCESS FLOWS    -   11. IMPLEMENTATION MECHANISMS—HARDWARE OVERVIEW    -   12. ENUMERATED EXAMPLE EMBODIMENTS, EQUIVALENTS, EXTENSIONS,        ALTERNATIVES AND MISCELLANEOUS        1. General Overview

This overview presents a basic description of some aspects of anembodiment of the present invention. It should be noted that thisoverview is not an extensive or exhaustive summary of aspects of theembodiment. Moreover, it should be noted that this overview is notintended to be understood as identifying any particularly significantaspects or elements of the embodiment, nor as delineating any scope ofthe embodiment in particular, nor the invention in general. Thisoverview merely presents some concepts that relate to the exampleembodiment in a condensed and simplified format, and should beunderstood as merely a conceptual prelude to a more detailed descriptionof example embodiments that follows below.

Human vision may not perceive a difference between two luminance valuesif the two luminance values are not sufficiently different from eachother. Instead, human vision only perceives a difference if theluminance value differ no less than a just noticeable difference (JND).Due to perceptual nonlinearity of human vision, the amounts ofindividual JNDs are not uniformly sized or scaled across a range oflight levels, but rather vary with different individual light levels. Inaddition, due to the perceptual nonlinearity, the amounts of individualJNDs are not uniformly sized or scaled across a range of spatialfrequencies at a particular light level, but rather vary with differentspatial frequencies below a cut-off spatial frequency.

Encoded image data with luminance quantization steps of equal sizes orlinearly scaled sizes does not match with perceptual nonlinearity ofhuman vision. Encoded image data with luminance quantization steps at afixed spatial frequency also does not match with perceptual nonlinearityof human vision. Under these techniques, when code words are assigned torepresent quantized luminance values, too many code words may bedistributed in a particular region (e.g., the bright region) of therange of light levels, while too few code words may be distributed in adifferent region (e.g., the dark region) of the range of light levels.

In the overpopulated region, a multitude of code words may not produceperceptual differences, and are, for all practical purposes, thereforewasted. In the underpopulated region, two adjacent code words mayproduce a perceptual difference much greater than a JND, and possiblyproduces contour distortion (also known as banding) visual artifacts.

Under techniques as described herein, a contrast sensitivity function(CSF) model may be used to determine JNDs across a wide range (e.g., 0to 12,000 cd/m²) of light levels. In an example embodiment, the peak JNDas a function of spatial frequency at a particular light level isselected to represent a quantum of human perception at the particularlight level. The selection of peak JNDs is in accord with the behaviorsof human vision that adapts to a heightened level of visualperceptibility when a background of close but different luminance valuesis being viewed, which is sometimes referred to in video and imagedisplay fields as a crispening effect and/or Whittle's Crispening effectand may be described herein as such. As used herein, the term “a lightadaption level” may be used to refer to a light level at which a (e.g.,peak) JND is selected/determined, assuming that human vision is adaptedto the light level. Peak JNDs as described herein vary over spatialfrequency at different light adaptation levels.

As used herein, the term “spatial frequency” may refer to a rate ofspatial modulation/variation in images (wherein rate is computed inrelation to or over spatial distance, in contrast to computing rate inrelation to time). In contrast to conventional approaches that may fixspatial frequency at a specific value, the spatial frequency asdescribed herein may vary, for example, in or over a range. In someembodiments, peak JNDs may be limited within a particular spatialfrequency range (e.g., 0.1 to 5.0, 0.01 to 8.0 cycles/degrees, or asmaller or larger range).

A reference gray scale display function (GSDF) may be generated based onthe CSF model. In some embodiments, a very wide field of view is assumedfor the CSF model for generating a reference GSDF that better supportentertainment display fields. The GSDF refers to a set of referencedigital code values (or reference code words), a set of reference graylevels (or reference luminance values), and a mapping between the twosets. In an example embodiment, each reference digital code valuecorresponds to a quantum of human perception, as represented by a JND(e.g., a peak JND at a light adaptation level). In an exampleembodiment, an equal number of reference digital code values maycorrespond to a quantum of human perception.

The GSDF may be obtained by accumulating JNDs from an initial value. Inan example embodiment, a middle code word value (e.g., 2048 for a 12-bitcode space) is given as an initial value to a reference digital code.The initial value of the reference digital code may correspond to aninitial reference gray level (e.g., 100 cd/m²). Other reference graylevels for other values of the reference digital code may be obtained bypositively accumulating (adding) JNDs as the reference digital code isincremented one by one, and by negatively accumulating (subtracting)JNDs as the reference digital code is decremented one by one. In anexample embodiment, quantities such as contrast thresholds may be usedin computing reference values in the GSDF, in place of JNDs. Thesequantities actually used in computation of a GSDF may be defined asunitless ratios and may differ from corresponding JNDs only by known ordeterminable multipliers, dividing factors and/or offsets.

A code space may be selected to include all reference digital codevalues in the GSDF. In some embodiments, the code space in which all thereference digital code values reside may be one of a 10-bit code space,an 11-bit code space, a 12-bit code space, a 13-bit code space, a 14-bitcode space, a 15-bit code space, or a larger or smaller code space.

While a large code space (>15 bits) may be used to host all referencedigital code values, in a particular embodiment, the most efficient codespace (e.g., 10 bits, 12 bits, etc.) is used to host all referencedigital code values generated in a reference GSDF.

The reference GSDF may be used to encode image data, for example,captured or generated by HDR cameras, studio systems, or other systemswith a scene-referred HDR that is significantly greater than dynamicranges of most if not all display devices. The encoded image data may beprovided to downstream devices in a wide variety of distribution ortransmission methods (e.g., HDMI video signals with 8 bit RGB, YCbCr, ordeep color options; 1.5 Gbps SDI video signals with a 10 bit 4:2:2sampling rate; 3 Gbps SDI with a 12 bit 4:4:4 or 10 bit 4:2:2 samplingrate; and other video or image formats).

In some embodiments, because adjacent reference digital code values inthe reference GSDF correspond to gray levels that are within a JND,details for which human vision is capable of distinguishing may becompletely or substantially preserved in the image data encoded based onthe reference GSDF. A display that fully supports the reference GSDF maypossibly render images with no banding or contour distortion artifacts.

Image data encoded based on the reference GSDF (or reference encodedimage data) may be used to support a wide variety of less capabledisplays that may not fully support all reference luminance values inthe reference GSDF. Because the reference encoded image data comprisesall the perceptual details in the supported luminance range (which maybe designed to be a superset of what displays support), referencedigital code values may be optimally and efficiently transcoded todisplay-specific digital code values in a way to preserve as muchdetails as a specific display is capable of supporting and to cause asfew visually noticeable errors as possible. Additionally and/oroptionally, decontouring and dithering may be performed in conjunctionwith, or as a part of, transcoding from reference digital code values todisplay-specific digital code values to further improve image or videoquality.

Techniques as described herein are not color-space dependent. They maybe used in a RGB color space, a YCbCr color space, or a different colorspace. Furthermore, techniques that derive reference values (e.g.,reference digital code values and reference gray levels) using JNDswhich vary with spatial frequency may be applied to a different channel(e.g., one of red, green, and blue channels) other than a luminancechannel in a different color space (e.g., RGB) which may or may notcomprise a luminance channel. For example, reference blue values may bederived in place of reference gray levels using JNDs which areapplicable to the blue color channel. Thus, in some embodiments, grayscale may be substituted for color. Additionally and/or optionally,different CSF models may also be used instead of Barten's model. So maydifferent model parameters be used for the same CSF model.

In some embodiments, mechanisms as described herein form a part of amedia processing system, including, but not limited to: a handhelddevice, game machine, television, laptop computer, netbook computer,cellular radiotelephone, electronic book reader, point of sale terminal,desktop computer, computer workstation, computer kiosk, or various otherkinds of terminals and media processing units.

Various modifications to the preferred embodiments and the genericprinciples and features described herein will be readily apparent tothose skilled in the art. Thus, the disclosure is not intended to belimited to the embodiments shown, but is to be accorded the widest scopeconsistent with the principles and features described herein.

2. Contrast Sensitivity Function (CSF) Model

Human visual sensitivity for spatial structures in rendered images maybe best described with contrast sensitivity functions (CSFs), whichdescribe contrast sensitivity as functions of spatial frequency (or rateof spatial modulation/variation in images as perceived by a humanobserver). As used herein, contrast sensitivity, S, may be considered asa gain in human visual neural signal processing, while contrastthresholds, C_(T), may be determined from the inverse of the contrastsensitivity, for example:Contrast-Sensitivity=S=1/C _(T)  expression (1)

As used herein, the term “contrast threshold” may refer to, or relateto, a lowest value (e.g., a just-noticeable difference) of (relative)contrast necessary for human eyes to perceive a difference in contrast;in some embodiments, contrast thresholds may also be depicted as afunction of the just-noticeable difference divided by the lightadaptation level across a range of luminance values.

In some embodiments, contrast thresholds may be directly measured inexperiments, without use of any CSF model. In some other embodiments,however, contrast thresholds may be determined based on a CSF model. ACSF model may be built with a number of model parameters and may be usedto derive a GSDF whose quantization steps in gray levels depend on andvary with light levels characterized by luminance values and spatialfrequency. An example embodiment may be implemented based on one or moreof a variety of CSF models such as those described in Peter G. J.Batten, Contrast Sensitivity of the Human Eye and its Effects on ImageQuality (1999) (herein after Barten's model or Barten's CSF model), orScott Daly, Chapter 17 in Digital Images and Human Vision, ed., by A. B.Watson, MIT Press (1993) (hereinafter Daly's model). In relation toexample embodiments of the present invention, contrast thresholds usedto generate a reference grayscale display function (GSDF) may be derivedexperimentally, theoretically, with a CSF model, or a combinationthereof.

As used herein, a GSDF may refer to a mapping of a plurality of digitalcode values (e.g., 1, 2, 3, . . . , N) to a plurality of gray levels(L₁, L₂, L₃, . . . , L_(N)), in which the digital code values representindex values of contrast thresholds and the gray levels correspond tothe contrast thresholds, as shown in TABLE 1.

TABLE 1 Digital Gray Level Code Value (Luminance Value) 1 L₁ 2 L₂ 3 L₃ .. . . . . i − 1 L_(i−1) I L_(i) i + 1 L_(i+1) . . . . . . N L_(N)

In an embodiment, a gray level (e.g., L_(i)) corresponding to a digitalcode value (e.g., i) and an adjacent gray level (e.g., L_(i+1)) may becomputed in relation to a contrast (e.g., C(i)) as follows:

$\begin{matrix}\begin{matrix}{{C(i)} = {\left( {L_{i + 1} - L_{i}} \right)/\left( {L_{i + 1} + L_{i}} \right)}} \\{= {\left( {L_{i + 1} - {L_{mean}\left( {i,{i + 1}} \right)}} \right)/{L_{mean}\left( {i,{i + 1}} \right)}}} \\{= {{{\sim 1}/2}\mspace{14mu}\Delta\;{L/L}}}\end{matrix} & {{expression}\mspace{14mu}(2)}\end{matrix}$wherein C(i) represents a contrast for a luminance range that is boundedbetween L_(i) and L_(i+1). L_(mean)(i, i+1) comprise an arithmeticaverage or mean of the two adjacent gray levels L_(i) and L_(i+1). Thecontrast C(i) is arithmetically related to a Weber fraction ΔL/L by afactor of two. Here, ΔL represents (L_(i+1)−L_(i)), and L represents oneof L_(i), L_(i+1), or an intermediate value between L_(i) and L_(i+1).

In some embodiments, a GSDF generator may set the contrast C(i) to avalue equal, or otherwise proportional, to a contrast threshold (e.g.,C_(T)(i)) at a luminance level L between L_(i) and L_(i+1), inclusive,as follows:C(i)=kC _(T)(i)  expression (3)wherein k represents a multiplicative constant. In relation toembodiments of the present invention, other descriptivestatistics/definitions (e.g., geometric mean, medium, mode, variance, orstandard deviation) and/or scaling (×2, ×3, divided or multiplied by ascaling factor, etc.) and/or offsetting (+1, +2, −1, −2, subtracted oradded by an offset, etc.) and/or weighting (e.g., assigning the twoadjacent gray levels with the same or different weight factors) may beused to relate contrast thresholds with contrasts for the purpose ofcomputing gray levels in a GSDF.

As computed in expressions (1), (2) and (3), contrasts or contrastthresholds may comprise a relative value, and may thus comprise aunitless quantity (e.g., so S may also be unitless).

A CSF model may be built up from basic contrast threshold measurementsor computations based on a CSF that depicts the CSF model. Human visionis unfortunately complex, adaptive and nonlinear, so that the there isno single CSF curve that describes the human vision. Instead, a familyof CSF curves may be generated based on a CSF model. Even with the sameCSF model, different values of model parameters produce different plotsfor the family of CSF curves.

3. Perceptual Nonlinearity

FIG. 1 illustrates an example family of CSF curves that span across aplurality of light adaptation levels. For the purpose of illustrationonly, the highest CSF curve depicted in FIG. 1 is for a light adaptationlevel at a luminance value of 1000 candelas per square meter (cd/m² or‘nits’), and the other decreasing height curves are for light adaptationlevels at decreasing luminance values with successive factors of 10reductions. Notable features readable from the CSF curves are that withincreasing luminance (increasing light adaptation levels), the overallcontrast sensitivity including the maximum (or peak) contrastsensitivity increases. The peak spatial frequency at which the contrastsensitivity peaks on the CSF curves in FIG. 1 shifts to higher spatialfrequencies. Similarly, the max perceptible spatial frequency (cut-offfrequency) on the CSF curves, which is the interception of the CSFcurves with the horizontal (spatial frequency) axis, also increases.

In an example embodiment, a CSF function that gives rise to a family ofCSF curves as illustrated in FIG. 1 may be derived with the Barten's CSFmodel, which takes into account a number of key effects relating tohuman perception. An example CSF, S(u), (or the inverse of thecorresponding contrast threshold, m_(t)) under the Barten's CSF modelmay be computed as shown in Expression (4), below.

$\begin{matrix}\begin{matrix}{{S(u)} = \frac{1}{m_{i}}} \\{= \frac{\left( {{M_{upi}(u)}/k} \right)}{\sqrt{\frac{2}{T}\left( {\frac{1}{X_{0}^{2}} + \frac{1}{X_{\max}^{2}} + \frac{u^{2}}{N_{\max}^{2}}} \right)\left( {\frac{1}{\eta\;{pE}} + \frac{\Phi_{0}}{1 - {\mathbb{e}}^{- {({u/u_{0}})}^{2}}}} \right)}}}\end{matrix} & {{expression}\mspace{14mu}(4)}\end{matrix}$The example model parameters used in expression (4) above comprise therepresentations listed below:

-   -   2 (the numeric factor) corresponds to binocular vision (4 if        monocular);    -   k represents a signal/noise ratio, for example, 3.0;    -   T represents an integration time of the eye, for example, 0.1        second;    -   X₀ represents an angular size of object (e.g., in a square        shape);    -   X_(max) represents a maximum angular size of the integration        area of the eye (e.g., 12 degrees);    -   N_(max) represents a maximum number of cycles that are        accumulated via probability summation, e.g., 15 cycles;    -   η represents a quantum efficiency of the eye, e.g., 0.03;    -   p represents a photon conversion factor,    -   E represents a retinal illuminance, for example, in Troland        units;    -   Φ₀ represents a spectral density of neural noise, e.g., 3×10⁻⁸        second*degrees²; and    -   u₀ represents a maximum spatial frequency for lateral        inhibition, e.g., 7 cycles/degrees.        The optical modulation transfer function, M_(opt), may be given        as follows:

$\begin{matrix}{= {\mathbb{e}}^{- 2_{{\pi\sigma}\; u}^{222}}} & {{expression}\mspace{14mu}(5)}\end{matrix}$where σ represents a model parameter related to pupil and/or lightlevel.

Barten's CSF model as discussed above may be used to describe perceptualnonlinearity relative to luminance. Other CSF models may also be used todescribe perceptual nonlinearity. For example, Barten's CSF model doesnot account for the effect of accommodation, which causes a lowering ofthe cut-off spatial frequency in the high spatial frequency region ofthe CSF. This lowering effect due to accommodation may be expressed as afunction of decreasing viewing distance.

For example, for viewing distances over 1.5 meters, the maximum cutoffspatial frequency as depicted by Barten's CSF model may be achieved,without affecting the effectiveness of Barten's model as an appropriatemodel to describe perceptual nonlinearity. However, for distances lessthan 1.5 meters, the effect of accommodation starts to becomesignificant, reducing the accuracy of Barten's model.

Thus, for tablet displays, which have closer viewing distances, such as0.5 meter, and smartphones, which can have viewing distances as close as0.125 meter, Barten's CSF model may not be optimally tuned.

In some embodiments, Daly's CSF model, which takes into account theaccommodation effect, may be used. In a particular embodiment, Daly'sCSF model may be constructed in part based on Barten's CSF, S(u), inexpression (4) above, for example, by modifying the optical modulationtransfer function, M_(opt), in expression (5).

4. Digital Code Values and Gray Levels

A GSDF as illustrated in TABLE 1 maps perceptual nonlinearity using thedigital code values to represent gray levels tied to contrast thresholdsin human vision. The gray levels which comprise all the mapped luminancevalues may be distributed in such a way that they are optimally spacedto match the perceptual nonlinearity of human vision.

In some embodiments, when the maximum number of gray levels in a GSDFare sufficiently large relative to the maximum range of luminancevalues, digital code values in the GSDF may be used in a way to achievethe lowest number (e.g., below a total of 4096 digital code values) ofgray levels without causing the visibility of the gray level steptransition (e.g., visible as a false contour or band in an image; or acolor shift in dark regions of an image).

In some other embodiments, a limited number of digital code values maystill be used to represent a wide dynamic range of gray levels. Forexample, when the maximum number of grayscale levels in a GSDF are notsufficiently large relative to the maximum range of the grayscale levels(e.g., digital code values in an 8-bit representation with the range ofgrayscale levels from 0 to 12,000 nits), the GSDF may still be used in away to achieve the lowest number (e.g., below a total of 256 digitalcode values) of gray levels to reduce or minimize the visibility of thegray level step transition. With such a GSDF, amounts/degrees ofperceptible errors/artifacts of the step transition may be evenlydistributed throughout the hierarchy of a relatively low number of graylevels in the GSDF. As used herein, the term “grayscale level” or “graylevel” may be used interchangeably, and may refer to a representedluminance value (a quantized luminance value represented in a GSDF).

Gray levels in a GSDF may be derived by stacking or integrating contrastthresholds across light adaptation levels (at different luminancevalues). In some embodiments, quantization steps between gray levels maybe so chosen that a quantization step between any two adjacent graylevels lands within a JND. A contrast threshold at a particular lightadaptation level (or luminance value) may be no more than thejust-noticeable difference (JND) at that particular adaptation level.Gray levels may be derived by integrating or stacking fractions ofcontrast thresholds (or JNDs). In some embodiments, the number ofdigital code values is more than sufficient to represent all the JNDs inthe represented dynamic range of luminance.

Contrast thresholds, or inversely contrast sensitivities, that are usedto compute grayscale levels may be selected from a CSF curve at adifferent spatial frequency other than a fixed spatial frequency for aparticular light adaptation level (or luminance value). In someembodiments, each of the contrast thresholds is selected from a CSFcurve at a spatial frequency that corresponds to a peak contrastsensitivity (e.g., due to Whittle's crispening effect) for a lightadaptation level. In addition, contrast thresholds may be selected fromCSF curves at different spatial frequencies for different lightadaptation levels.

An example expression to compute/stack the gray levels in the GSDF is asfollows:

$\begin{matrix}{{{G\; S\; D\; F} = \left( {\sum\limits_{Lmin}{JND}} \right)}{{J\; N\; D} = {1/{S\left( {f,L_{1}} \right)}}}} & {{expression}\mspace{14mu}(6)}\end{matrix}$where f represents the spatial frequency, which may be other than afixed number under techniques as described herein; and L_(A) representsthe light adaptation level. L_(min) may be the lowest luminance value inall the mapped gray levels. As used herein, the term “Nit” or itsabbreviation “nt” may relate or refer, synonymously or interchangeably,to a unit of image intensity, brightness, luma and/or luminance that isequivalent or equal to one (1) candela per square meter (1 Nit=1 nt=1cd/m²). In some embodiments, L_(min) may comprise a value of zero. Insome other embodiments, L_(min) may comprise a non-zero value (e.g., acertain dark black level, 10⁻⁵ nit, 10⁻⁷ nit, etc., which may be lowerthan what display devices are generally able to achieve). In someembodiments, L_(min) may be replaced with other than a minimum initialvalue, such as an intermediate value, or a maximum value, which allowsstacking computations with subtraction or negative addition.

In some embodiments, stacking of the JNDs to derive gray levels in aGSDF is performed by summation, for example, as shown in expression (6).In some other embodiments, an integral may be used in place of thediscrete summation. The integral may integrate along an integration pathdetermined from a CSF (e.g., expression (4)). For example, theintegration path may comprise peak contrast sensitivities (e.g.,different peak sensitivities corresponding to different spatialfrequencies) for all light adaptation levels in a (reference) dynamicrange for the CSF.

As used herein, an integration path may refer to a visible dynamic range(VDR) curve used to represent human perceptual nonlinearity and toestablish a mapping between a set of digital code values and a set ofreference gray levels (quantized luminance values). The mapping may berequired to meet the criteria that each quantization step (e.g., theluminance difference of two adjacent gray levels in TABLE 1) be lessthan the JNDs above or below a corresponding light adaptation level(luminance value). The instantaneous derivative (in units ofnit/spatial-cycle) of the integration path at a particular lightadaptation level (luminance value) is proportional to the JND at theparticular adaptation level. As used herein, the term “VDR” or “visualdynamic range” may refer a dynamic range wider than a standard dynamicrange, and may include, but is not limited to, a wide dynamic range upto the instantaneously perceivable dynamic range and color gamut whichhuman vision can perceive at an instant.

Based on techniques as described herein, a reference GSDF that isindependent of any specific displays or image processing devices may bedeveloped. In some embodiments, one or more model parameters other thanlight adaptation level (luminance), spatial frequency, and angular sizemay be set to constant (or fixed) values.

5. Model Parameters

In some embodiments, the CSF model is constructed with conservativemodel parameter values that cover a broad range of display devices. Theuse of the conservative model parameter values provides smaller JNDsthan existing standard GSDFs. Accordingly, in some embodiments, thereference GSDF under the techniques described herein is capable ofsupporting luminance values with a high precision that exceeds therequirements of these display devices.

In some embodiments, model parameters as described herein include afield-of-vision (FOV) parameter. The FOV parameter may be set to a valueof 45 degrees, 40 degrees, 35 degrees, 30 degrees, 25 degrees, oranother larger or smaller value that supports a wide range of displaydevices and viewing scenarios including those used in studios, theatersor high-end entertainment systems.

Model parameters as described herein may include an angular sizeparameter, which may relate for example to a field of view. The angularsize parameter may be set to a value of 45 degrees×45 degrees, 40degrees×40 degrees, 35 degrees×35 degrees, 30 degrees×30 degrees, 25degrees×25 degrees, or another larger or smaller value that supports awide range of display devices and viewing scenarios. In someembodiments, the angular size parameter used in part to derive thereference GSDF is set to n degrees×m degrees, where either of n and mmay be a numeric value between 30 and 40, and n and m may or may not beequal.

In some embodiments, a larger angular size (e.g., 40 degrees×40 degrees)is used to produce a reference GSDF with a greater number of grayscalelevels and thus more contrast sensitivity. The GSDF may be used tosupport a wide range of viewing and/or displaying scenarios (e.g., largescreen video displays) which may require a wide viewing angle of ˜30 to40 degrees. The GSDF having an increased sensitivity due to theselection of large angular size may also be used to support highlyvariable viewing and/or displaying scenarios (e.g., cinemas). It ispossible to select even larger angular sizes; however, raising theangular size significantly above a certain angular size (e.g., 40degrees) may produce relatively limited marginal benefits.

In some embodiments, a reference GSDF model covers a large luminancerange. For example, gray levels, or quantized luminance values, that arerepresented by the reference GSDF model ranges from 0 or approximately 0(e.g., 10⁻⁷ cd/m²) to 12,000 cd/m². The lower bound of the representedluminance values in the reference GSDF model may be 10⁻⁷ cd/m², or alower or higher value (e.g., 0, 10⁻⁵, 10⁻⁸, 10⁻⁹ cd/m², etc.). The GSDFmay be used to support a wide range of viewing and/or displayingscenarios with different ambient light levels. The GSDF may be used tosupport a wide range of display devices with different dark black levels(in theaters, indoor, or outdoor).

The upper bound of the represented luminance values in the referenceGSDF model may be 12,000 cd/m², or a lower or higher value (e.g.,6000-8000, 8000-10000, 10000-12000, 12000-15000 cd/m², etc.). The GSDFmay be used to support a wide range of viewing and/or displayingscenarios with high dynamic ranges. The GSDF may be used to support awide range of display devices with different maximum luminance levels(HDR TVs, SDR displays, laptops, tablets, handheld devices, etc.).

6. Variable Spatial Frequencies

FIG. 2 illustrates an example integration path (denoted as VDR) that maybe used as an integration path for obtaining gray levels in a referenceGSDF as described herein, in accordance with an example embodiment ofthe present invention. In embodiments, the VDR curve is used toaccurately capture the peak contrast sensitivity of human vision over ahigh dynamic range of luminance values.

As illustrated in FIG. 2, peak contrast sensitivities do not occur at afixed spatial frequency value, but rather occur at smaller spatialfrequencies as light adaptation levels (luminance values) drop. Thismeans that techniques (e.g., DICOM) with a fixed spatial frequency maysignificantly underestimate contrast sensitivities of human vision forthe dark light adaptation levels (low luminance values). Lower contrastsensitivities give rise to higher contrast thresholds, resulting inlarger quantization step sizes in quantized luminance values.

Unlike the Digital Imaging and Communications in Medicine (DICOM)standard, a VDR curve under techniques as described herein does not fixthe spatial frequency model parameter at a fixed value such as 4 cyclesper degree. Rather, the VDR curve varies with the spatial frequency andaccurately captures the peak contrast sensitivities of human vision at aplurality of light adaptation levels. The VDR curve properly takes intoaccount the crispening effect due to human vision's adaptability to awide range of light adaptation levels, and helps generate ahigh-precision reference GSDF. Here, the term “high-precision” meansthat perceptual errors due to quantization of luminance values areremoved or substantially reduced based on a reference GSDF that best andmost efficiently captures human visual nonlinearity within theconstraint of a fixed size code space (e.g., one of 10 bits, 12 bits,etc.).

A computation process may be used to calculate gray levels in thereference GSDF (e.g., TABLE 1). In an example embodiment, thecomputation process is iterative or recursive, repeatedly determines thecontrast thresholds (or modulation threshold, for example, m, inexpression 4) from the VDR curve, and applies the contrast thresholds toobtain successive gray levels in the reference GSDF. This computationprocess may be implemented with the following expressions (7):

$\begin{matrix}{{m_{i} = {{\frac{L_{\max} - L_{\min}}{L_{\max} + L_{\min}}\mspace{14mu}{so}\text{:}\mspace{14mu} L_{j + 1}} = {L_{j}\frac{1 + m_{i}}{1 - m_{i}}}}}{and}{L_{j - 1} = {L_{j}\frac{1 - m_{i}}{1 + m_{i}}}}} & {{expressions}\mspace{14mu}(7)}\end{matrix}$where j−1, j and j+1 represent indexes to three adjacent digital codevalues; L_(j−1), L_(j) and L_(j+1) correspond to gray levels to whichthe digital code values j−1, j and j+1 are mapped, respectively. L_(max)and L_(min) respectfully represent maximum luminance value and minimumluminance value across a JND or a fraction of a JND. Using a JND or afraction thereof maintains the high precision of the reference GSDF.

The contrast threshold m, associated with the JND may be defined as arelative quantity, e.g., a difference between L_(max) and L_(min), asdivided by a particular luminance value of either L_(max) or L_(min), orin between L_(max) and L_(min) (e.g., an average of L_(max) andL_(min)). In some embodiments, m_(i) may be alternatively defined as thedifference between L_(min) and L_(min), as divided by a multiplier(e.g., 2) of a particular luminance value of either L_(max) or L_(min),or in between L_(max) and L_(min). In quantizing luminance values in aGSDF to a plurality of gray levels, L_(max) and L_(min) may refer toadjacent gray levels in the plurality of gray levels. As a result, L_(j)may be related to L_(j−1) and L_(j+1), through m₁, respectively, asshown in expression (7).

In alternative embodiments, instead of using linear expressions asillustrated in expression (7), non-linear expression may be used torelate JNDs or contrast thresholds with gray levels. For example, analternative expression based on the standard deviation divided by themean may be used in place of a simple ratio for the contrast thresholdas illustrated.

In some embodiments, a reference GSDF covers a range of 0 to 12,000cd/m² with digital code values represented as 12-bit integer value. Tofurther improve the precision of the reference GSDF, m, may bemultiplied with a fraction value f. Furthermore, a center digital valueL2048 (note that the digital code values are at least limited to 0 and4096 as in a 12-bit code space that is compatible with SDI) may bemapped to 100 cd/m². Expression (7) may yield the following expression(8):

$\begin{matrix}{{L_{2048} = {100\mspace{14mu}{{cd}/m^{2}}}}{L_{j + 1} = {L_{j}\frac{1 + {f*m_{i}}}{1 - {f*m_{i}}}}}{and}{L_{j - 1} = {L_{j - 1} = {L_{j}\frac{1 - {f*m_{i}}}{1 + {f*m_{i}}}}}}} & {{expression}\mspace{14mu}(8)}\end{matrix}$wherein the fraction value f is set to 0.918177. In the exampleembodiment, the minimum allowed value for the digital codes is set tocode word (or integer value) 16 is set to 0 (cd/m²). The second lowestdigital code value 17 ends up at 527×10⁻⁷ cd/m², while the digital codevalue 4076 ends up at 12,000 cd/m².

FIG. 3 illustrates an example GSDF that maps between a plurality of graylevels (in logarithmic luminance values) and a plurality of digital codevalues in a 12-bit code space, in accordance with an example embodimentof the present invention.

FIG. 4 illustrates a curve depicting Weber fractions (Delta L/L, orΔL/L) based on gray levels of the example GSDF of FIG. 3. Perceptualnonlinearity of human vision as illustrated by FIG. 4 is represented asa function of luminance values on a logarithmic luminance axis.Comparable visual differences (e.g., JNDs) of human vision correspond tolarger Delta L/L values at lower luminance values. The curve of Weberfractions asymptotes to a constant value for high luminance values(e.g., a Weber fraction of 0.002 where Weber's law is met at higherluminance values).

7. Functional Models

One or more analytical functions may be used to obtain a mapping betweendigital code values and gray levels in a GSDF (reference GSDF ordevice-specific GSDF) as described herein. The one or more analyticalfunctions may be proprietary, standard-based, or extensions fromstandard-based functions. In some embodiments, a GSDF generator (e.g.,504 of FIG. 5) may generate a GSDF in the form of one or more forwardlook-up tables (LUTs) and/or one or more inverse LUTs based on the oneor more analytical functions (or formulas). At least some of these LUTsmay be provided to a variety of image data codecs (e.g., 506 of FIG. 5)or a wide variety of display device to be used in converting betweenreference gray levels and reference digital code levels for the purposeof encoding reference image data. Additionally, optionally, oralternatively, at least some of the analytical functions (with theircoefficients in integer or floating point representations) may bedirectly provided to image data codecs or a wide variety of displaydevice to be used in obtaining mappings between digital code values andgray levels in a GSDF as described herein and/or converting between graylevels and digital code levels for the purpose of encoding image data.

In some embodiments, analytical functions as described herein comprise aforward function that may be used to predict a digital code value basedon a corresponding gray level, as follows:

$\begin{matrix}{D = \left\lbrack \frac{c_{1} + {c_{2}L^{n}}}{1 + {c_{3}L^{n}}} \right\rbrack^{m}} & {{expression}\mspace{14mu}(9)}\end{matrix}$where D represents a (e.g., 12 bit) value of digital code, L representsa luminance value or gray level in nits, n may represent a slope in amiddle section of a log D/log L curve as given by expression (9), m mayrepresent the sharpness of the knee of the log D/log L curve, and c1, c2and c3 may define the end and middle points of the log D/log L curve.

In some embodiments, the analytical functions comprise an inversefunction that corresponds to the forward function in expression (9) andmay be used to predict a luminance value based on a correspondingdigital code value, as follows:

$\begin{matrix}{L = \left\lbrack \frac{D^{1/m} - c_{1}}{c_{2} - {c_{3}D^{1/m}}} \right\rbrack^{1/n}} & {{expression}\mspace{14mu}(10)}\end{matrix}$

Digital code values predicted based on a plurality of luminance valuesusing expression (9) may be compared with observed digital code values.The observed digital code values may be, but are not limited only to anyof, numeric calculation based on a CSF model as previously discussed. Inan embodiment, a deviation between the predicted digital code values andthe observed digital code values may be computed and minimized to deriveoptimal values of the parameters n, m, c₁, c₂, and c₃ in expression (9).

Likewise, luminance values predicted based on a plurality of digitalcode values using expression (10) may be compared with observedluminance values. The observed luminance values may, but are not limitedto, be generated using numeric computations based on a CSF model aspreviously discussed, or using human visual experimentation data. In anembodiment, the deviation between the predicted luminance values and theobserved luminance values may be derived as a function of the parametersn, m, c₁, c₂, and c₃ and minimized to derive optimal values of theparameters n, m, c₁, c₂, and c₃ in expression (10).

A set of optimal values of the parameters n, m, c₁, c₂, and c₃ asdetermined with expression (9) may or may not be the same as a set ofoptimal values of the parameters n, m, c₁, c₂, and c₃ as determined withexpression (10). In case of differences between the two sets, one orboth of the two sets may be used to generate a mapping between digitalcode values and luminance values. In some embodiments, the two sets ofoptimal values of the parameters n, m, c₁, c₂, and C₃, if different, maybe harmonized, for example, based on minimization of round trip errors,which are introduced by performing both forward and inverse codingoperations with both expressions (9) and (10). In some embodiments,multiple round trips may be made to study resultant errors in digitalcode values and/or in luminance values or gray levels. In someembodiments, selection of the parameters in expressions (9) and (10) maybe based at least in part on a criterion that no significant erroroccurs in one, two, or more round trips. Examples of no significantround trip errors may include, but are not limited only to any of,errors smaller than 0.0001%, 0.001%, 0.010%, 0.1%, 1%, 2%, or otherconfigurable values.

Embodiments include using a code space of one of one or more differentbit lengths to represent digital control values. Optimized values of theparameters in expressions (9) and (10) may be obtained for each of aplurality of code spaces each with a different one of one of one or moredifferent bit lengths. Based on the optimized values of expressions (9)and (10), distributions of code errors (e.g., forward transformationerrors, inverse transformation errors or round trip errors in digitalcode values based on expressions (9) and (10)) may be determined. Insome embodiments, a numeric difference of one (1) in two digital codevalues corresponds to a contrast threshold (or corresponds to a JND) ata light level between two luminance values represented by the twodigital code values. FIG. 10A illustrates maximums for code errors inunits of JNDs in a plurality of code spaces each with a different one ofone of one or more different precisions (with different bit lengths),according to some example embodiments. For example, based on functionalmodels as described herein, the maximum code error for a code space ofinfinite or unlimited bit length is 11.252. In comparison, based on afunctional model as described herein, the maximum code error for a codespace of a 12 bit length (or 4096) is 11.298. This indicates that a codespace of a 12 bit length for digital code values is an excellent choicewith a functional model as represented by expressions (9) and (10).

FIG. 10B illustrates a distribution of code errors for a code space ofthe 12 bit length (or 4096) with a forward transformation (fromluminance values to digital code values) as specified by expression (9),according to an example embodiment. FIG. 10C illustrates a distributionof code errors for a code space of the 12 bit length (or 4096) with abackward transformation (from digital code values to luminance values)as specified by expression (10), according to an example embodiment.Both FIG. 10B and FIG. 10C indicate maximum code errors of less than12.5.

FIG. 11 illustrates values of parameters that may be used in expressions(9) and (10), according to an example embodiment. In some embodiments,as illustrated, integer-based formulas may be used torepresent/approximate these non-integer values in a specificimplementation of a functional model as described herein. In some otherembodiments, fixed point, floating point values with one of one or moreprecisions (e.g., 14-, 16-, or 32 bits) may be used to represent thesenon-integer values in a specific implementation of a functional model asdescribed herein.

Embodiments include using a functional model with formulas other thanthose (which may be tone-mapping curves) given in expressions (9) and(10). For example, a cone model with a Naka-Rushton formula as followsmay be used by a functional model as described herein:

$\begin{matrix}{L_{d} = \left\lbrack {L_{d}^{\max}\left( \frac{L^{n}}{\sigma + L^{n}} \right)} \right\rbrack^{m}} & {{expression}\mspace{14mu}(11)}\end{matrix}$wherein L represent luminance values, n, m and σ represent modelparameters in association with the cone model, and, L_(d) representspredicted values that may be encoded with digital code values. Similarmethods of obtaining model parameters through minimizing deviations maybe used to derive optimal values of the model parameters for expression(11). FIG. 10D illustrates a distribution of code errors for a codespace of the 12 bit length (or 4096) with a forward transformation (fromluminance values to digital code values) as specified by expression(11), according to an example embodiment. In an embodiment, the maximumcode error as illustrated in FIG. 10D is 25 JNDs.

In another example, a functional model may be generated with a Raised muformula as follows:

$\begin{matrix}{y = \left( {1 + \mu} \right)^{x^{1 + {({1 - x})}^{6.2}}}} & {{expression}\mspace{14mu}(12)}\end{matrix}$wherein x represents luminance values, and y represents predicteddigital code values. An optimal value of the model parameter μ may beobtained through minimizing deviations. FIG. 10E illustrates adistribution of code errors for a code space of the 12 bit length (or4096) with a forward transformation (from luminance values to digitalcode values) as specified by expression (12), according to an exampleembodiment. In an embodiment, the maximum code error as illustrated inFIG. 10D is 17 JNDs.

As illustrated herein, in some embodiments, a functional model may beused to predict code values from luminance values or predict luminancevalues from code values. Formulas used by the functional model may beinvertible. Same or similar processing logic may be implemented toperform forward and inverse transformation between these values. In someembodiments, model parameters including but not limited only to any ofexponents may be represented by fixed-point values or integer-basedformulas. Thus, at least a part of the processing logic may beefficiently implemented in hardware only, software only, or acombination of hardware and software. Similarly, at least a part of LUTsgenerated with the functional model or model formulas (such asexpressions (9) through (12)) may be efficiently implemented in hardwareonly, software only, or a combination of hardware and software(including ASIC or FPGA). In some embodiments, one, two, or morefunctional models may be implemented in a single computing device, aconfiguration of multiple computing devices, a server, etc. In someembodiments, errors in predicted code values may be within 14 codevalues of target or observed values over a full range of visible dynamicrange of luminance values. In some embodiments, this holds true for bothforward and inverse transformations. Same or different sets of modelparameters may be used in forward and inverse transformations.Round-trip accuracy may be maximized with optimal values of the modelparameters. Different code spaces may be used. In particular embodimenta code space of 12 bit length (4096) may be used to host digital codevalues with minimal code errors across the full range of visible dynamicrange.

As used herein, a reference GSDF may refer to a GSDF comprisingreference digital code values and reference gray levels as related undera functional model (the model parameters of which may be determined withtarget or observed values under a CSF model), as determined with numericcomputations (e.g., without determining any functional representation ofa mapping between digital code values and luminance values) based on aCSF model, or as determined with data from human visual studies. In someembodiments, a device GSDF may also comprise a mapping between digitalcode values and gray levels that may be analytically represented with afunctional model as described herein.

8. Exchange Image Data Based on Reference GSDF

For the purpose of illustration, it has been described that digital codevalues reside in a 12 bit code space. The present invention, however, isnot so limited. Digital code values with different code spaces (e.g.,different bit depths other than 12 bits) may be used in a referenceGSDF. For example, 10 bit integer values may be used to representdigital codes. Instead of mapping a digital code value 4076 to aluminance value 12000 cd/m² in a 12-bit representation of digital codes,a digital code value 1019 may be mapped to the luminance value 12000cd/m² in a 10-bit representation of digital codes. Thus, these and othervariations in code spaces (bit depths) may be used for digital codevalues in a reference GSDF.

The reference GSDF may be used to exchange image data across differentGSDFs which may be individually designed for each type of imageacquisition device or image rendering device. For example, a GSDFimplemented with a specific type of image acquisition device or imagerendering device may implicitly or explicitly depend on model parametersthat do not match model parameters of a standard GSDF or adevice-specific GSDF with another type of image acquisition device orimage rendering device.

A reference GSDF may correspond to curve shapes as depicted in FIG. 3and FIG. 4. Generally speaking, the shapes of GSDFs depend on parametersused to derive or design the GSDFs. Hence, a reference GSDF depends on areference CSF model and reference model parameters used to generate thereference GSDF from the reference CSF model. The curve shape of adevice-specific GSDF depends on the specific device, including displayparameters and viewing conditions if the specific device is a display.

In an example, a display whose supported range of luminance values islimited to less than 500 cd/m² may not experience the increase in slopeat a high luminance value region (which occurs when the human visionshifts to a logarithmic behavior for all frequencies) as shown in FIG.3. Driving the display with a curve shape of FIG. 3 may lead tononoptimal (e.g., suboptimal) allocation of gray levels, with too manygray levels allocated in the bright regions, and not enough allocated inthe dark regions.

In another example, a low contrast display is designed to be usedoutdoors in various daylight conditions. The display's luminance rangemay occur largely or almost entirely in the log behavior region of FIG.3. Driving this low contrast display with a curve shape of FIG. 3 mayalso lead to nonoptimal (suboptimal) allocation of gray levels, with toomany gray levels allocated in the dark regions, and not enough allocatedin the bright regions.

Under techniques as described herein, each display may use its specificGSDF (dependent on not only the display parameters, but also on theviewing conditions which, for example, affect the actual black level) tooptimally support perceptual information in image data encoded with areference GSDF. The reference GSDF is used by one or more upstream(e.g., encoding) devices for the overall encoding of image data topreserve perceptual details as much as possible. The image data encodedin the reference GSDF is then delivered to one or more downstream (e.g.,decoding) devices. In an example embodiment, encoding of image databased on the reference GSDF is independent of specific devices that areto subsequently decode and/or render the image data.

Each device (e.g., display) has its specific GSDF where device-specificgray levels are supported/optimized. The specific gray levels may beknown to the maker of the display, or may have been specificallydesigned by the maker to support the device-specific GSDF (which may ormay not be standard based). The line driver of the device may beimplemented with quantized luminance values specific to the device.Optimization may be best done for the device based on the quantizedluminance values specific to the device. Additionally, the dark blacklevel (e.g., the lowest device-specific gray level), which may be usedas the lower bound to the range of device-specific gray levels, may beset based in part on the present ambient light level and/or the device'soptical reflectivity (which may be known to the maker). Once the darkblack level is so set, device-specific gray levels may be obtained orset by implicitly or explicitly accumulating (e.g.,stacking/integrating) quantization steps in the line driver of thedevice. The derivation and/or adjustment of gray levels may or may notbe done at runtime when the device is concurrently rendering images.

Thus, under techniques as described herein, embodiments of the presentinvention may include, but are not limited only to, encoding image datawith a reference GSDF and decoding and rendering the image data with adisplay-specific GSDF.

Techniques as described herein may be used to exchange image data acrossa variety of devices with different GSDFs. FIG. 5 illustrates an exampleframework (500) of exchange image data with devices of different GSDFs,in accordance with an example embodiment of the present invention. Asillustrated in FIG. 5, an adaptive CSF model (502) may be used togenerate a reference GSDF (504). The term “adaptive” may refer to theadaptability of a CSF model to human visual nonlinearity and behaviors.The adaptive CSF model may be built based at least in part on aplurality of CSF parameters (or model parameters). The plurality ofmodel parameters include, for example, light adaptation level, displayarea in degree width, noise level, accommodation (physical viewingdistance), luminance or color modulation vector (which may be, forexample, related to test images or image patterns used in the adaptiveCSF model (502)).

An upstream (e.g., encoding) device may receive image data to be encodedwith the reference GSDF (504) before the image data or its derivative istransmitted or distributed to downstream (e.g., decoding) devices. Theimage data to be encoded may initially be in any of a plurality offormats (standard based, proprietary, extension thereof, etc.) and/ormay be derived from any of a plurality of image sources (camera, imageserver, tangible media, etc.). Examples of image data to be encodedinclude, but are not limited only to, raw or other high bit-depthimage(s) 530. The raw or other high bit-depth image(s) may come from acamera, a studio system, an art director system, another upstream imageprocessing system, an image server, a content database, etc. The imagedata may include, but is not limited only to, that of digital photos,video image frames, 3D images, non-3D images, computer-generatedgraphics, etc. The image data may comprise scene-referred images,device-referred images, or images with various dynamic ranges. Examplesof image data to be encoded may include a high-quality version oforiginal images that are to be edited, down-sampled, and/or compressed,along with metadata, into a coded bitstream for distribution to imagereceiving systems (downstream image processing system such as displaysof various makers). The raw or other high bit-depth image(s) may be of ahigh sampling rate used by a professional, an art studio, a broadcastcompany, a high-end media production entity, etc. Image data to beencoded may also be in whole or in part computer generated, or may evenbe obtained based in whole or in part from existing image sources suchas old movies and documentaries.

As used herein, the phrase “image data to be encoded” may refer to imagedata of one or more images; the image data to be encoded may comprisefloating-point or fixed-point image data, and may be in any color space.In an example embodiment, the one or more images may in an RGB colorspace. In another example embodiment, the one or more images may be in aYIN color space. In an example, each pixel in an image as describedherein comprises floating-point pixel values for all channels (e.g.,red, green, and blue color channels in the RGB color space) defined inthe color space. In another example, each pixel in an image as describedherein comprises fixed-point pixel values for all channels (e.g., 16bits or higher/lower numbers of bits fixed-point pixel values for red,green, and blue color channels in the RGB color space) defined in thecolor space. Each pixel may optionally and/or alternatively comprisedownsampled pixel values for one or more of the channels in the colorspace.

In some embodiments, in response to receiving the image data to beencoded, an upstream device in the framework (500) maps luminance valuesas specified by or determined from the image data to reference digitalcode values in the reference GSDF, and generates, based on the imagedata to be encoded, reference encoded image data encoded with thereference digital code values. The mapping operation, from the luminancevalues based on the image data to be encoded to the reference digitalcode values, may include selecting reference digital code values whosecorresponding reference gray levels (e.g., as shown in TABLE 1) match,or approximate as closely as any other reference luminance values in thereference GSDF, the luminance values as specified by or determined fromthe image data to be encoded and replacing the luminance values with thereference digital code values in the reference encoded image data.

Additionally, optionally or alternatively, preprocessing and postprocessing steps (which may include, but are not limited only to, colorspace conversion, down sampling, upsampling, tone mapping, colorgrading, decompression, compression, etc.) may be performed as a part ofgenerating the reference encoded image data.

In an example embodiment, the framework (500) may comprise softwareand/or hardware components (e.g., an encode or format unit (506))configured to encode and/or format the reference encoded image data intoone or more coded bitstreams or image files. The coded bitstreams orimage files may be in a standard-based format, a proprietary format, oran extension format based at least in part on a standard-based format.Additionally and/or optionally, the coded bitstreams or image files maycomprise metadata containing one or more of related parameters (e.g.,model parameters; minimum luminance value, maximum luminance value,minimum digital code value, maximum digital code value, etc., asillustrated in TABLE 1, FIG. 3 and FIG. 4; an identifying field thatidentifies a CSF among a plurality of CSFs; reference viewing distance)related to the reference GSDF, pre-processing or post processing used togenerate the reference encoded image data.

In some embodiments, the framework (500) may comprise one or morediscrete upstream devices. For example, at least one of the one or moreupstream devices in the framework (500) may be configured to encodeimage data based on the reference GSDF. The upstream devices maycomprise software and/or hardware components configured to perform thefunctionality related to 502, 504, and 506, of FIG. 5. The codedbitstreams or image files may be outputted by the upstream devices (502,504, and 506, of FIG. 5) through network connections, digitalinterfaces, tangible storage media, etc., and delivered in an image dataflow (508) to other image processing devices for processing orrendering.

In some example embodiments, the framework (500) further comprises oneor more downstream devices as one or more discrete devices. Thedownstream devices may be configured to receive/access, from the imagedata flow (508), the coded bitstreams or image files outputted by theone or more upstream devices. For example, the downstream devices maycomprise software and/or hardware components (e.g., a decode or reformatunit (510)) configured to decode and/or reformat the coded bitstreamsand image files, and recover/retrieve the reference encoded image datatherein. As illustrated in FIG. 5, the downstream devices may comprise adiverse set of display devices.

In some embodiments, a display device (not shown) may be designed and/orimplemented to support the reference GSDF. High-precision HDR imagerendering may be provided if the display device supports each and everygray level in the reference GSDF. The display device may render imagesat details at a finer level than, or at the same level as, what humanvision may possibly detect.

In some embodiments, a display device's native digital code values(which may be implemented as digitized voltage values, e.g., digitaldrive levels or DDLs, in the display system) in a device-specific GSDFmay correspond to device-specific gray levels (or luminance values)different from those in the reference GSDF. The device-specific graylevels may be designed to support sRGB, Rec. 709, or otherspecifications including those using representations related tocomplementary densities. Additionally, optionally, or alternatively, thedevice-specific gray levels may be based on the essential DACcharacteristics of display driving.

In some embodiments, a display device A (512-A) may be designed and/orimplemented to support a device-specific GSDF A (514-A) of a visibledynamic range (VDR) display. GSDF A (514-A) may be based on a bit depthof 12 bits (a 12 bit code space) for device-specific digital codevalues, a 10,000:1 contrast ratio (CR), and a >P3 gamut. GSDF A (514-A)may support gray levels within a first sub-range (e.g., 0 to 5,000cd/m²) in the entire range of the reference GSDF (504). Alternativelyand/or optionally, GSDF A (514-A) may support the entire range (0 to12,000 cd/m², for example) in the reference GSDF (504) but may comprisefewer than all the reference gray levels in the reference GSDF (504).

In some embodiments, a display device B (512-B) may be designed and/orimplemented to support a device-specific GSDF B (514-B) for a dynamicrange narrower than the VDR. For example, display device B (512-B) maybe a standard dynamic range (SDR) display. As used herein, the terms“standard dynamic range” and “low dynamic range,” and/or theircorresponding abbreviations “SDR” and “LDR” may be used synonymouslyand/or interchangeably. In some embodiments, GSDF B (514-B) may supporta bit depth of 8 bits for device-specific digital code values, a500-5,000:1 contrast ratio (CR), and a color gamut as defined in Rec.709. In some embodiments, GSDF B (514-B) may provide gray levels withina second sub-range (e.g., 0 to 2000 cd/m²) of the reference GSDF (504).

In some embodiments, a display device C (512-C) may be designed and/orimplemented to support a device-specific GSDF C (514-C) for a dynamicrange even narrower than the SDR. For example, display device C (512-C)may be a tablet display. In some embodiments, GSDF C (514-C) may supporta bit depth of 8 bits for device-specific digital code values, a100-800:1 contrast ratio (CR), and a color gamut smaller than thatdefined in Rec. 709. In some embodiments, GSDF C (514-C) may supportgray levels within a third sub-range (e.g., 0 to 1,200 cd/m²) of thereference GSDF (504).

In some embodiments, a display device (e.g., display device D (512-D))may be designed and/or implemented to supports a device-specific GSDF(e.g., GSDF D (514-D)) for a very limited dynamic range much narrowerthan the SDR. For example, display device D (512-D) may comprise ane-paper display. In some embodiments, GSDF D (514-D), may support a bitdepth of 6 bits or less for device-specific digital code values; acontrast ratio (CR) of 10:1 or less, and a color gamut much smaller thanthat defined in Rec. 709. In some embodiments, GSDF D (514-D) maysupport gray levels within a fourth sub-range (e.g., 0 to 100 cd/m²) ofthe reference GSDF (504).

Precision in image rendering may be gracefully scaled down with each ofdisplay devices A through D (512-A through -D). In some embodiments, thesubset of gray levels in each of device specific GSDF A through D (514-Athrough -D) may be correlated with, or mapped to, supported referencegray levels in the reference GSDF (504) in such a way as to evenlydistribute perceptually noticeable errors in the range of gray levelssupported by that display device.

In some embodiments, a display device (e.g., one of 512-A through -D)with a device-specific GSDF (e.g., one of 514-A through -D)receives/extracts reference encoded image data encoded based on areference GSDF. In response, the display device, or a conversion unit(one of 516-A through -D) therein, maps reference digital code values asspecified in the reference encoded image data, to device-specificdigital code values that are native to the display device. This may beperformed in one of several ways. In an example, mapping from thereference digital code values to the device-specific digital code valuesincludes selecting device-specific gray levels (corresponding to thedevice-specific digital code values) that match, or approximate asclosely as any other device-specific gray levels, the reference graylevels (corresponding to the reference digital code values). In anotherexample, mapping from the reference digital code values to thedevice-specific digital code values includes (1) determining tone-mappedluminance values based on the reference gray levels (corresponding tothe reference digital code values) associated with the reference GSDF,and (2) selecting device-specific gray levels (corresponding to thedevice-specific digital code values) that match, or approximate asclosely as any other device-specific gray levels, the tone-mappedluminance values.

Subsequently, the display device, or a driver chip (one of 518-A through-D) therein, may use the display-specific digital code values to renderimages with device-specific gray levels that correspond to thedisplay-specific code values.

Generally speaking, a reference GSDF may be based on a different CSFmodel than that on which a display-specific GSDF is based.Conversion/mapping between the reference GSDF and the device-specificGSDF is necessary. Even if the same CSF model is used to generate boththe reference GSDF and a device-specific GSDF, different values of modelparameters may be used in deriving the GSDFs. For the reference GSDF,model parameter values may be conservatively set to preserve details fora wide variety of downstream devices, while for the device-specificGSDF, model parameter values may reflect specific design/implementationand viewing conditions under which the display device is to renderimages. Conversion/mapping between the reference GSDF and thedevice-specific GSDF is still necessary, as the specific displaydevice's viewing condition parameters (e.g., the ambient light level,the display device's optical reflectivity, etc.) are different from themodel parameter values used to derive the reference GSDF. Here, theviewing condition parameters may include those that impinge displayquality (e.g., contrast ratio, etc.) and elevate the black level (e.g.,the lowest gray level, etc.). Conversion/mapping between the referenceGSDF and the device-specific GSDF under techniques as described hereinimproves quality in image rendering (e.g., improve the contrast ratio byincreasing luminance values at high value regions, etc.).

9. Converting Reference Encoded Data

FIG. 6 illustrates an example conversion unit (e.g., 516), in accordancewith some embodiments of the present invention. The conversion unit(516) may, but is not limited only to, be one (e.g., 516-A) of aplurality of conversion units (e.g., 516-A through -D) as illustrated inFIG. 5. In some embodiments, the conversion unit (516) may receive firstdefinition data for a reference GSDF (REF GSDF) and second definitiondata for a device-specific GSDF (e.g., GSDF-A (514-A of FIG. 5)). Asused herein, the terms “device-specific” and “display-specific” may beused interchangeably, if the device is a display.

Based on the definition data received, the conversion unit (516)cascades the reference GSDF with display-specific GSDF to form aconversion lookup table (Conversion LUT). Cascading between the twoGSDFs may include comparing gray levels in the two GSDFs, and based onthe results of comparing gray levels, establishing a mapping betweenreference digital code values in the reference GSDF and display-specificdigital code values in the display-specific GSDF.

More specifically, given a reference digital code value in the referenceGSDF, its corresponding reference gray level may be determined based onthe reference GSDF. The reference gray level so determined may be usedto locate a device-specific gray level in the display-specific GSDF. Inan example embodiment, the device-specific gray level located may match,or approximate as closely as any other display-specific gray levels inthe display-specific GSDF, the reference gray level. In another exampleembodiment, a tone-mapped luminance value may be obtained by a global orlocal tone-mapping operator acting on the reference gray level; thedevice-specific gray level located may match, or approximate as closelyas any other display-specific gray levels in the display-specific GSDF,the tone-mapped luminance value.

With the device-specific gray level, a corresponding display-specificdigital code value may be identified from the display-specific GSDF. Anentry may be added or defined in the conversion LUT, consisting of thereference digital code value and the display-specific code value.

The steps as described above may be repeated for other reference digitalcode values in the reference GSDF.

In some embodiments, a conversion LUT may be pre-built and stored beforeimage data whose processing is to be done based in part on theconversion LUT is received and processed. In alternative embodiments,image data that is to be processed with a conversion LUT is analyzed.The results of the analysis may be used to set up or at least adjustcorrespondence relationships between the reference digital code valuesand the device-specific digital code values. For example, if the imagedata indicates a particular concentration or distribution of luminancevalues, the conversion LUT may be set up in a way to preserve a largeamount of details in the concentrated region of luminance values.

In some embodiments, the conversion unit (516) comprises one or moresoftware and/or hardware components (a comparison sub-unit (602))configured to compare quantization steps (e.g., luminance valuedifferences, or ΔLs, between adjacent digital code values) in both thereference GSDF and display-specific GSDF (514-A). For example, thequantization step at a reference digital code value in the referenceGSDF may be a reference luminance value difference (reference GSDF ΔL),while the quantization step at a display-specific digital code value inthe display-specific GSDF may be a display-specific luminance valuedifference (display-specific GSDF ΔL). Here, the display-specificdigital code value corresponds to (or forms a pair in the conversion LUTwith) the reference digital code value. In some embodiments, thecomparison sub-unit (602) compares these two luminance valuedifferences. This operation is essentially a test which may be performedeither based on ΔL values, or optionally and/or alternatively, based onthe relative slopes of the two GSDF curves.

Quantization steps for luminance values in the display-specific GSDF maytypically exceed those of the reference GSDF, as one or more referencegray levels from the reference GSDF (e.g., corresponding to a highbit-depth domain, etc.) are merged into display-specific gray levelsfrom the display-specific GSDF (e.g., corresponding to a low bit-depthdomain, etc.). In these cases, dithering is used to remove bandingartifacts. As part of overall dithering, dithering is also performed onlocal surrounding output pixels (in space and/or in time). In a sense,the human eye may be represented as a low-pass filter. At least in thissense, averaging local surrounding pixels as described herein thuscreates desired output gray levels that reduce and/or remove bandingvisual artifacts, which otherwise could be present due to largequantization steps in the display-specific GSDF.

In less common cases, quantization steps for luminance values for thereference GSDF may occasionally exceed those of the display-specificGSDF. A decontouring algorithm-based process is used, synthesizing anoutput gray level based on an input gray level, for example, byaveraging neighboring input pixels.

Correspondingly, if the reference GSDF ΔL is greater than thedisplay-specific GSDF ΔL, which is the “Y” path in FIG. 6, then adecontour algorithm flag is set for an entry, in the conversion LUT,that comprises the reference digital code value and the display-specificdigital code value.

If the reference GSDF ΔL is less than the display-specific GSDF ΔL,which is the “N” path in FIG. 6, then a dither algorithm flag is set foran entry, in the conversion LUT, that comprises the reference digitalcode value and the display-specific digital code value.

If the reference GSDF ΔL is equal to the display-specific GSDF ΔL, thenneither a decontour algorithm flag nor a dither algorithm flag is setfor an entry, in the conversion LUT, that comprises the referencedigital code value and the display-specific digital code value.

Decontour and dither algorithm flags may be stored with entries in theconversion LUT, or may be stored in a related data structure outside,but operatively linked with, the conversion LUT.

In some embodiments, the conversion unit (516) is configured to receivereference encoded image data, which may be in the form of high bit-depthor floating point input image, and to map reference digital code valuesspecified in the reference GSDF to display-specific digital code valuesspecified in the display-specific GSDF. In addition to mapping digitalcode values between the GSDFs, the conversion unit (516) may beconfigured to perform decontouring or dithering based on the settings ofalgorithm flags (decontour algorithm flags or dithering algorithm flags)previously discussed.

As noted, the reference GSDF likely contains a greater amount of detailsthan a display-specific GSDF; thus, the “Y” path of FIG. 6 may notoccur, or may occur less often. In some embodiments, the “Y” path andrelated processing may be omitted to simplify the implementation of aconversion unit.

In some embodiments, given a reference digital code value as determinedfor a pixel in the reference encoded image data, the conversion unit(516) looks up in the conversion LUT for a correspondingdisplay-specific digital code value, and replaces the reference digitalcode value with the corresponding display-specific digital code value.Additionally and/or optionally, the conversion unit (516) determineswhether a decontour or dithering algorithm should be performed for thepixel, based on the existence/setting of an algorithm flag for an entry,in the conversion LUT, that comprises the reference digital code valueand the display-specific digital code value.

If it is determined that neither a decontour algorithm nor a ditheringalgorithm should be performed (e.g., no indication or flag forperforming either algorithm), then no decontour or dithering isperformed for the pixel for the time being.

If it is determined that a decontour algorithm should be performed, thenthe conversion unit (516) may perform one or more decontour algorithms(Decontour Algo). Performing the one or more decontour algorithms mayinclude receiving image data of input local neighborhood pixels andinputting the image data of the local neighborhood pixels to thedecontour algorithms.

If it is determined that a dithering algorithm should be performed, thenthe conversion unit (516) may perform one or more dithering algorithms(Dithering Algo).

The pixel may still be involved in decontour or dithering if theconversion unit (516) determines that decontour or dithering needs to beperformed with respect to neighborhood pixels. In an example, thedevice-specific (output) gray level of the pixel may be used fordithering local neighborhood pixels. In another example, the reference(input) gray level of the pixel may be used for decontouring localneighborhood pixels.

In some embodiments, the conversion unit (516) outputs the processingresults of the foregoing steps to downstream processing units orsub-units. The processing results comprise display-specific encodedimage data in the format of display-specific bit-depth output imageencoded with digital code values in the display-specific GSDF (e.g.,GSDF-A).

FIG. 7 illustrates an example SDR display (700) which implements 8 bitimage processing. The SDR display (700), or a VDR decode unit (702)therein, receives an encoded input. The encoded input comprisesreference coded image data in an image data container which may be inone of a plurality of image data container formats. The VDR decode unit(702) decodes the encoded input and determines/retrieves the referenceencoded image data from therein. The reference encoded image data maycomprise image data for individual pixels in a color space (e.g., a RGBcolor space, a YCbCr color space, etc.). The image data for individualpixels may be encoded with reference digital code values in a referenceGSDF.

Additionally and/or optionally, the SDR display (700) comprises adisplay management unit (704) that maintains display parameters for theSDR display (700). The display parameters may at least in part define adisplay-specific GSDF (e.g., GSDF-B of FIG. 5) associated with the SDRdisplay (700). The display parameters defining the display-specific GSDFmay include maximum (max) and minimum (min) gray levels supported by theSDR display (700). The display parameters may also include colorprimaries (primaries) supported by the SDR display, display size (size),optical reflectivity of the SDR display's image rendering surface,ambient light level. Some of the display parameters may be preconfiguredwith fixed values. Some of the display parameters may be measured inreal-time or near real-time by the SDR display (700). Some of thedisplay parameters may be configurable by a user of the SDR display(700). Some of the display parameters may be preconfigured with defaultvalues and may be overridden by measurement or by a user. The displaymanagement unit (704) establishes/shapes perceptual nonlinearity of thedisplay-specific gray levels based on the reference GSDF, and mayadditionally and/or optionally perform tone mapping as a part ofestablishing/shaping the display-specific gray levels. For example, aconversion LUT as illustrated in FIG. 5 and/or other related meta data(e.g., dithering and decontour processing flags, etc.) may beestablished by the display management unit (704) for the purpose ofestablishing/shaping perceptual nonlinearity of the display-specificgray levels in accordance with the reference GSDF. Cascading operationsas previously discussed may be implemented with the display managementunit (704) to create the conversion LUT and/or other related metadata(712) relating to one or both of the reference GSDF and display-specificGSDF. The conversion LUT and/or other related metadata (712) may beaccessed and used by other units or sub-units in the SDR display (700).Further, the conversion LUT and/or other related metadata may be usedas, or to derive, metadata (714) for inverting perceptual nonlinearity.As used herein, inverting perceptual nonlinearity may include convertingdisplay-specific digital code values to display-specific digital drivinglevels (e.g., digitized voltage levels in the display device).

Additionally and/or optionally, the SDR display (700) includes aconversion unit (516) as illustrated in FIG. 5 and FIG. 6, and an 8 bitperceptual quantizer (706). In some embodiments, the SDR display (700),or the conversion unit (516) and the 8 bit perceptual quantizer (706)therein, converts the reference encoded image data into adisplay-specific bit-depth output image encoded with display-specificdigital code values associated with the display-specific GSDF (e.g.,GSDF-A or GSDF-B of FIG. 5), and quantizes the display-specificbit-depth output image into perceptually encoded image data in a 8 bitcode space. As used herein, the term “perceptually encoded” may refer toa type of encoding that is based on a human visual perceptual model,such as a CSF that gives rise to the reference GSDF.

Additionally and/or optionally, the SDR display (700) comprises a videopost-processing unit (708) that may, but is not limited only to, performzero, one, or more of image processing operations on the perceptuallyencoded image data in an 8 bit luminance representation. These imageprocessing operations may include, but are not limited only to,compression, decompression, color space conversion, downsampling,upsampling, or color grading. The results of these operations may beoutputted to other parts of the SDR display (700).

In an example embodiment, the SDR display (700) comprises an 8 bitinverse perceptual quantizer (710) configured to convertdisplay-specific digital code values in the results of image processingoperations to display-specific digital driving levels (e.g., digitizedvoltage levels). The display-specific digital driving levels generated(or converted back from digital code values) by the inverse perceptualquantizer (710) may specifically support one of several types ofluminance nonlinearities supportable in the SDR display (700). In anexample, the inverse perceptual quantizer (710) convertsdisplay-specific digital code values to display-specific digital drivinglevels to support luminance nonlinearities associated with Rec. 709. Inanother example, the inverse perceptual quantizer (710) convertsdisplay-specific digital code values to display-specific digital drivinglevels to support luminance nonlinearities associated with a linearluminance domain or a log luminance domain (which may be relatively easyto be integrated with local dimming operations). In another example, theinverse perceptual quantizer (710) converts display-specific digitalcode values to display-specific digital driving levels to support adisplay-specific CSF (or its associated GSDF), with optimal placement ofdisplay-specific gray levels for the specific display (700), andpossibly adjusted for the viewing conditions specific to the display(700).

10. Example Process Flows

FIG. 8A illustrates an example process flow according to an embodimentof the present invention. In some embodiments, one or more computingdevices or components such as one or more computing devices in framework(500) may perform this process flow. In block 802, a computing devicereceives image data to be encoded.

In block 804, the computing device encodes, based on a reference mappingbetween a set of reference digital code values and a set of referencegray levels, the image data to be encoded into reference encoded imagedata. Here, luminance values in the image data to be encoded arerepresented by the set of reference digital code values. A luminancedifference between two reference gray levels represented by two adjacentreference digital code values in the set of reference digital codevalues may be inversely proportional to a peak contrast sensitivity ofhuman vision adapted at a particular light level.

In block 806, the computing device outputs the reference encoded imagedata.

In an embodiment, the computing device determines a reference gray scaledisplay function (GSDF) based on a contrast sensitivity function (CSF)model; the reference GSDF specifies the reference mapping between theset of reference digital code values and the set of reference graylevels. The CSF model comprises one or more model parameters, which mayhave an angular size that falls in a range comprising one or more of:between 25 degrees×25 degrees and 30 degrees×30 degrees, between 30degrees×30 degrees and 35 degrees×35 degrees, between 35 degrees×35degrees and 40 degrees×40 degrees, between 40 degrees×40 degrees and 45degrees×45 degrees, or greater than 45 degrees×45 degrees.

In an embodiment, the computing device assigns an intermediate luminancevalue, within a range of luminance values supported by the set ofreference gray levels, to an intermediate digital code value in a codespace that hosts the set of reference digital code values, and derives,by performing one or more of stacking or integration computations, aplurality of sub-mappings, each sub-mapping maps a reference digitalcode value in the set of reference digital code values to a referencegray level in the set of reference gray levels. The intermediateluminance value may be selected within a range comprising one or moreof: less than 50 nits, between 50 nits and 100 nits inclusive, between100 and 500 nits inclusive, or no less than 500 nits.

In an example embodiment, the set of reference gray levels covers adynamic range with an upper limit having a value of: less than 500 nits,between 500 nits and 1000 nits inclusive, between 1000 and 5000 nitsinclusive, between 5000 nits and 10000 nits inclusive, between 10000nits and 15000 nits inclusive, or greater than 15000 nits.

In an embodiment, the peak contrast sensitivity is determined from acontrast sensitivity curve among a plurality of contrast sensitivitycurves determined based on a contrast sensitivity function (CSF) modelhaving model parameters comprising one or more of a luminance valuevariable, a spatial frequency variable, or one or more other variables.

In an embodiment, at least two peak contrast sensitivities determinedbased on at least two contrast sensitivity curves in the plurality ofcontrast sensitivity curves occur at two different spatial frequencyvalues.

In an embodiment, the computing device converts one or more input imagesrepresented, received, transmitted, or stored with the image data to beencoded from an input video signal into one or more output imagesrepresented, received, transmitted, or stored with the reference encodedimage data contained in an output video signal.

In an embodiment, the image data to be encoded comprises image dataencoded in one of a high-resolution high dynamic range (HDR) imageformat, a RGB color spaces associated with the Academy Color EncodingSpecification (ACES) standard of the Academy of Motion Picture Arts andSciences (AMPAS), a P3 color space standard of the Digital CinemaInitiative, a Reference Input Medium Metric/Reference Output MediumMetric (RIMM/ROMM) standard, an sRGB color space, a RGB color spaceassociated with the BT.709 Recommendation standard of the InternationalTelecommunications Union (ITU), etc.

In an embodiment, the luminance difference between the two referencegray levels represented by the two adjacent reference digital codevalues is less than a just noticeable difference threshold at theparticular light level.

In an embodiment, the particular light level is a luminance valuebetween the two luminance values, inclusive.

In an embodiment, the set of reference digital code values comprisesinteger values in a code space with a bit depth of: less than 12 bits;between 12 bits and 14 bits, inclusive; at least 14 bits; 14 bits ormore.

In an embodiment, the set of reference gray levels may comprise a set ofquantized luminance values.

FIG. 8B illustrates another example process flow according to anembodiment of the present invention. In some embodiments, one or morecomputing devices or components such as one or more computing devices inframework (500) may perform this process flow. In block 852, a computingdevice determines a digital code mapping between a set of referencedigital code values and a set of device-specific digital code values.Here, the set of reference digital code values is mapped in a referencemapping to a set of reference gray levels, while the set ofdevice-specific digital code values is mapped in a device-specificmapping to a set of device-specific gray levels.

In block 854, the computing device receives reference encoded image dataencoded with the set of reference digital code values. Luminance valuesin the reference encoded image data are based on the set of referencedigital code values. A luminance difference between two reference graylevels represented by two adjacent reference digital code values in theset of reference digital code values may be inversely proportional to apeak contrast sensitivity of human vision adapted at a particular lightlevel.

In block 856, the computing device transcodes, based on the digital codemapping, the reference encoded image data encoded with the set ofreference digital code values into device-specific image data encodedwith the set of device-specific digital control codes. Luminance valuesin the device-specific image data are based on the set ofdevice-specific digital code values.

In an embodiment, the computing device determines a set ofcorrespondence relationships between the set of reference digital codevalues and the set of device-specific digital code values. Here, acorrespondence relationship in the set of correspondence relationshiprelates a reference digital code value in the set of reference digitalcode values to a device-specific digital code value. The computingdevice further compares a first luminance difference at the referencedigital code value and a second luminance difference at thedevice-specific digital code value, and stores, based on comparing thefirst luminance difference and the second luminance difference, analgorithm flag as to whether dithering, decontouring, or no operationshould be performed for the reference digital code value.

In an embodiment, the computing device determines a reference digitalcode value from the reference encoded image data for a pixel, andfurther determines whether an algorithm flag is set for the referencedigital code value. In response to determining that an algorithm flag isset for decontour, the computing device performs a decontour algorithmon the pixel. Alternatively, in response to determining that analgorithm flag is set for dithering, the computing device performs adithering algorithm on the pixel.

In an embodiment, the computing device renders one or more images on adisplay based on the device-specific image data encoded with the set ofdevice-specific digital control codes. Here, the display may be, but isnot limited only to, one of a visible dynamic range (VDR) display, astandard dynamic range (SDR) display, a tablet computer display, or ahandheld device display.

In an embodiment, a device-specific gray scale display function (GSDF)specifies the device-specific mapping between the set of device-specificdigital code values and the set of device-specific gray levels.

In an embodiment, the device-specific mapping is derived based on one ormore display parameters and zero or more viewing condition parameters.

In an embodiment, the set of device-specific gray levels covers adynamic range with an upper limit having a value of: less than 100 nits,no less than 100 nits but less than 500 nits, between 500 nits and 1000nits inclusive, between 1000 and 5000 nits inclusive, between 5000 nitsand 10000 nits inclusive, or greater than 10000 nits.

In an embodiment, the computing device converts one or more input imagesrepresented, received, transmitted, or stored with the reference encodedimage data from an input video signal into one or more output imagesrepresented, received, transmitted, or stored with the device-specificimage data contained in an output video signal.

In an embodiment, the device-specific image data supports imagerendering in one of a high-resolution high dynamic range (HDR) imageformat, a RGB color spaces associated with the Academy Color EncodingSpecification (ACES) standard of the Academy of Motion Picture Arts andSciences (AMPAS), a P3 color space standard of the Digital CinemaInitiative, a Reference Input Medium Metric/Reference Output MediumMetric (RIMM/ROMM) standard, an sRGB color space, or a RGB color spaceassociated with the BT.709 Recommendation standard of the InternationalTelecommunications Union (ITU).

In an embodiment, the set of device-specific digital code valuescomprises integer values in a code space with a bit depth of: 8 bits;greater than 8 but less than 12 bits; 12 bits or more.

In an embodiment, the set of device-specific gray levels may comprise aset of quantized luminance values.

In various embodiments, an encoder, a decoder, a system, etc., performsany or a part of the foregoing methods as described.

11. Implementation Mechanisms—Hardware Overview

According to one embodiment, the techniques described herein areimplemented by one or more special-purpose computing devices. Thespecial-purpose computing devices may be hard-wired to perform thetechniques, or may include digital electronic devices such as one ormore application-specific integrated circuits (ASICs) or fieldprogrammable gate arrays (FPGAs) that are persistently programmed toperform the techniques, or may include one or more general purposehardware processors programmed to perform the techniques pursuant toprogram instructions in firmware, memory, other storage, or acombination. Such special-purpose computing devices may also combinecustom hard-wired logic, ASICs, or FPGAs with custom programming toaccomplish the techniques. The special-purpose computing devices may bedesktop computer systems, portable computer systems, handheld devices,networking devices or any other device that incorporates hard-wiredand/or program logic to implement the techniques.

For example, FIG. 9 is a block diagram that illustrates a computersystem 900 upon which an example embodiment of the invention may beimplemented. Computer system 900 includes a bus 902 or othercommunication mechanism for communicating information, and a hardwareprocessor 904 coupled with bus 902 for processing information. Hardwareprocessor 904 may be, for example, a general purpose microprocessor.

Computer system 900 also includes a main memory 906, such as a randomaccess memory (RAM) or other dynamic storage device, coupled to bus 902for storing information and instructions to be executed by processor904. Main memory 906 also may be used for storing temporary variables orother intermediate information during execution of instructions to beexecuted by processor 904. Such instructions, when stored innon-transitory storage media accessible to processor 904, rendercomputer system 900 into a special-purpose machine that is customized toperform the operations specified in the instructions.

Computer system 900 further includes a read only memory (ROM) 908 orother static storage device coupled to bus 902 for storing staticinformation and instructions for processor 904. A storage device 910,such as a magnetic disk or optical disk, is provided and coupled to bus902 for storing information and instructions.

Computer system 900 may be coupled via bus 902 to a display 912, such asa liquid crystal display, for displaying information to a computer user.An input device 914, including alphanumeric and other keys, is coupledto bus 902 for communicating information and command selections toprocessor 904. Another type of user input device is cursor control 916,such as a mouse, a trackball, or cursor direction keys for communicatingdirection information and command selections to processor 904 and forcontrolling cursor movement on display 912. This input device typicallyhas two degrees of freedom in two axes, a first axis (e.g., x) and asecond axis (e.g., y), that allows the device to specify positions in aplane.

Computer system 900 may implement the techniques described herein usingcustomized hard-wired logic, one or more ASICs or FPGAs, firmware and/orprogram logic which in combination with the computer system causes orprograms computer system 900 to be a special-purpose machine. Accordingto one embodiment, the techniques herein are performed by computersystem 900 in response to processor 904 executing one or more sequencesof one or more instructions contained in main memory 906. Suchinstructions may be read into main memory 906 from another storagemedium, such as storage device 910. Execution of the sequences ofinstructions contained in main memory 906 causes processor 904 toperform the process steps described herein. In alternative embodiments,hard-wired circuitry may be used in place of or in combination withsoftware instructions.

The term “storage media” as used herein refers to any non-transitorymedia that store data and/or instructions that cause a machine tooperation in a specific fashion. Such storage media may comprisenon-volatile media and/or volatile media. Non-volatile media includes,for example, optical or magnetic disks, such as storage device 910.Volatile media includes dynamic memory, such as main memory 906. Commonforms of storage media include, for example, a floppy disk, a flexibledisk, hard disk, solid state drive, magnetic tape, or any other magneticdata storage medium, a CD-ROM, any other optical data storage medium,any physical medium with patterns of holes, a RAM, a PROM, and EPROM, aFLASH-EPROM, NVRAM, any other memory chip or cartridge.

Storage media is distinct from but may be used in conjunction withtransmission media. Transmission media participates in transferringinformation between storage media. For example, transmission mediaincludes coaxial cables, copper wire and fiber optics, including thewires that comprise bus 902. Transmission media can also take the formof acoustic or light waves, such as those generated during radio-waveand infra-red data communications.

Various forms of media may be involved in carrying one or more sequencesof one or more instructions to processor 904 for execution. For example,the instructions may initially be carried on a magnetic disk or solidstate drive of a remote computer. The remote computer can load theinstructions into its dynamic memory and send the instructions over atelephone line using a modem. A modem local to computer system 900 canreceive the data on the telephone line and use an infra-red transmitterto convert the data to an infra-red signal. An infra-red detector canreceive the data carried in the infra-red signal and appropriatecircuitry can place the data on bus 902. Bus 902 carries the data tomain memory 906, from which processor 904 retrieves and executes theinstructions. The instructions received by main memory 906 mayoptionally be stored on storage device 910 either before or afterexecution by processor 904.

Computer system 900 also includes a communication interface 918 coupledto bus 902. Communication interface 918 provides a two-way datacommunication coupling to a network link 920 that is connected to alocal network 922. For example, communication interface 918 may be anintegrated services digital network (ISDN) card, cable modem, satellitemodem, or a modem to provide a data communication connection to acorresponding type of telephone line. As another example, communicationinterface 918 may be a local area network (LAN) card to provide a datacommunication connection to a compatible LAN. Wireless links may also beimplemented. In any such implementation, communication interface 918sends and receives electrical, electromagnetic or optical signals thatcarry digital data streams representing various types of information.

Network link 920 typically provides data communication through one ormore networks to other data devices. For example, network link 920 mayprovide a connection through local network 922 to a host computer 924 orto data equipment operated by an Internet Service Provider (ISP) 926.ISP 926 in turn provides data communication services through the worldwide packet data communication network now commonly referred to as the“Internet” 928. Local network 922 and Internet 928 both use electrical,electromagnetic or optical signals that carry digital data streams. Thesignals through the various networks and the signals on network link 920and through communication interface 918, which carry the digital data toand from computer system 900, are example forms of transmission media.

Computer system 900 can send messages and receive data, includingprogram code, through the network(s), network link 920 and communicationinterface 918. In the Internet example, a server 930 might transmit arequested code for an application program through Internet 928, ISP 926,local network 922 and communication interface 918.

The received code may be executed by processor 904 as it is received,and/or stored in storage device 910, or other non-volatile storage forlater execution.

12. Enumerated Example Embodiments, Equivalents, Extensions,Alternatives and Miscellaneous

Enumerated example embodiments (“EEEs”) of the present invention havebeen described above in relation to perceptual luminancenonlinearity-based image data exchange across displays of differentcapabilities. Thus, an embodiment of the present invention may relate toone or more of the examples, enumerated in Table 2 below.

TABLE 2 Enumerated Example Embodiments (EEE1.) A method, comprising:receiving image data to be encoded; encoding, based on a referencemapping between a set of reference digital code values and a set ofreference gray levels, the received image data into reference encodedimage data, wherein luminance values in the received image data arerepresented by the set of reference digital code values, wherein aluminance difference between two reference gray levels in the receivedimage data is represented by two adjacent reference digital code valuesin the set of reference digital code values, and wherein the luminancedifferent between the two adjacent reference digital code values isinversely proportional to a peak contrast sensitivity of human visionthat is adapted at a particular light level; and outputting thereference encoded image data. (EEE2.) The method as recited inenumerated example embodiment 1, further comprising determining areference gray scale display function (GSDF) based on a contrastsensitivity function (CSF) model, wherein the reference GSDF specifiesthe reference mapping between the set of reference digital code valuesand the set of reference gray levels. (EEE3.) The method as recited inenumerated example embodiment 2, wherein the CSF model comprises one ormore model parameters, and wherein the one or more model parameterscomprise an angular size that falls in a range comprising one or moreof: between 25 degrees × 25 degrees and 30 degrees × 30 degrees,inclusive, between 30 degrees × 30 degrees and 35 degrees × 35 degrees,inclusive, between 35 degrees × 35 degrees and 40 degrees × 40 degrees,inclusive, between 40 degrees × 40 degrees and 45 degrees × 45 degrees,inclusive, or greater than 45 degrees × 45 degrees. (EEE4.) The methodas recited in enumerated example embodiment 1, further comprising:assigning an intermediate luminance value, within a range of luminancevalues supported by the set of reference gray levels, to an intermediatedigital code value in a code space that hosts the set of referencedigital code values; and deriving, by performing one or more of stackingor integration computations, a plurality of sub-mappings, eachsub-mapping maps a reference digital code value in the set of referencedigital code values to a reference gray level in the set of referencegray levels. (EEE5.) The method as recited in enumerated exampleembodiment 4, wherein the intermediate luminance value is selectedwithin a range comprising one or more of: less than 50 nits, between 50nits and 100 nits, inclusive, between 100 and 500 nits, inclusive, orgreater than 500 nits. (EEE6.) The method as recited in enumeratedexample embodiment 1, wherein the set of reference gray levels covers adynamic range with an upper limit having a value of: less than 500 nits,between 500 nits and 1000 nits, inclusive, between 1000 and 5000 nits,inclusive, between 5000 nits and 10000 nits, inclusive, between 10000nits and 15000 nits, inclusive, or greater than 15000 nits. (EEE7.) Themethod as recited in enumerated example embodiment 1, wherein the peakcontrast sensitivity is determined from a contrast sensitivity curveamong a plurality of contrast sensitivity curves determined based on acontrast sensitivity function (CSF) model having model parameterscomprising one or more of a luminance value variable, a spatialfrequency variable, or one or more other variables. (EEE8.) The methodas recited in enumerated example embodiment 7, wherein at least two peakcontrast sensitivities determined based on at least two contrastsensitivity curves in the plurality of contrast sensitivity curves occurat two different spatial frequency values. (EEE9.) The method as recitedin enumerated example embodiment 1, further comprising converting one ormore input images represented, received, transmitted, or stored with theimage data to be encoded from an input video signal into one or moreoutput images represented, received, transmitted, or stored with thereference encoded image data contained in an output video signal.(EEE10.) The method as recited in enumerated example embodiment 1,wherein the image data to be encoded comprises image data encoded in oneof a high-resolution high dynamic range (HDR) image format, a RGB colorspace associated with the Academy Color Encoding Specification (ACES)standard of the Academy of Motion Picture Arts and Sciences (AMPAS), aP3 color space standard of the Digital Cinema Initiative, a ReferenceInput Medium Metric/Reference Output Medium Metric (RIMM/ROMM) standard,an sRGB color space, or a RGB color space associated with the BT.709Recommendation standard of the International Telecommunications Union(ITU). (EEE11.) The method as recited in enumerated example embodiment1, wherein the luminance difference between the two reference graylevels represented by the two adjacent reference digital code values isless than a just noticeable difference (JND) threshold at the particularlight level. (EEE12.) The method as recited in enumerated exampleembodiment 1, wherein the particular light level comprises a luminancevalue between the two luminance values, inclusive. (EEE 13.) The methodas recited in enumerated example embodiment 1, wherein the set ofreference digital code values comprises integer values in a code spacewith a bit depth of at least one of: less than 12 bits; between 12 bitsand 14 bits, inclusive; at least 14 bits; or 14 bits or more. (EEE14.)The method as recited in enumerated example embodiment 1, wherein theset of reference gray levels may comprise a set of quantized luminancevalues. (EEE15.) The method as recited in enumerated example embodiment1, wherein the reference GSDF is determined based at least in part on afunctional model represented with one or more functions. (EEE16.) Themethod as recited in enumerated example embodiment 15, wherein thefunctional model comprises one or more model parameters, and whereinvalues of the model parameters are optimized through minimizingdeviations between predicted code values and target code values.(EEE17.) A method, comprising the steps of: determining a digital codemapping between a set of reference digital code values and a set ofdevice-specific digital code values, wherein the set of referencedigital code values is mapped in a reference mapping to a set ofreference gray levels, and wherein the set of device-specific digitalcode values is mapped in a device-specific mapping to a set ofdevice-specific gray levels; receiving reference encoded image dataencoded with the set of reference digital code values, wherein luminancevalues in the reference encoded image data are based on the set ofreference digital code values, wherein a luminance difference betweentwo reference gray levels represented by two adjacent reference digitalcode values in the set of reference digital code values is inverselyproportional to a peak contrast sensitivity of human vision adapted at aparticular light level; and transcoding, based on the digital codemapping, the reference encoded image data encoded with the set ofreference digital code values into device-specific image data encodedwith the set of device-specific digital control codes, wherein luminancevalues in the device-specific image data are based on the set ofdevice-specific digital code values. (EEE18.) The method as recited inenumerated example embodiment 17, further comprising: determining a setof correspondence relationships between the set of reference digitalcode values and the set of device-specific digital code values, whereina correspondence relationship in the set of correspondence relationshiprelates a reference digital code value in the set of reference digitalcode values to a device-specific digital code value; comparing a firstluminance difference at the reference digital code value and a secondluminance difference at the device-specific digital code value; andstoring, based on comparing the first luminance difference and thesecond luminance difference, an algorithm flag as to whether dithering,decontouring, or no operation should be performed for the referencedigital code value. (EEE19.) The method as recited in enumerated exampleembodiment 17, further comprising: determining a reference digital codevalue from the reference encoded image data for a pixel; and determiningwhether an algorithm flag is set for the reference digital code value.(EEE20.) The method as recited in enumerated example embodiment 19,further comprising, in response to determining that an algorithm flag isset for decontour, performing a decontour algorithm on the pixel.(EEE21.) The method as recited in enumerated example embodiment 19,further comprising, in response to determining that an algorithm flag isset for dithering, performing a dithering algorithm on the pixel.(EEE22.) The method as recited in enumerated example embodiment 17,further comprising rendering one or more images on a display based onthe device-specific image data encoded with the set of device-specificdigital control codes, the display being one of a visible dynamic range(VDR) display, a standard dynamic range (SDR) display, a tablet computerdisplay, or a handheld device display. (EEE23.) The method as recited inenumerated example embodiment 17, wherein a device-specific gray scaledisplay function (GSDF) specifies the device-specific mapping betweenthe set of device-specific digital code values and the set ofdevice-specific gray levels. (EEE24.) The method as recited inenumerated example embodiment 17, wherein the device-specific mapping isderived based on one or more display parameters and zero or more viewingcondition parameters. (EEE25.) The method as recited in enumeratedexample embodiment 17, wherein the set of device-specific gray levelscovers a dynamic range with an upper limit having a value of: less than100 nits; no less than 100 nits but less than 500 nits; between 500 nitsand 1000 nits, inclusive; between 1000 and 5000 nits, inclusive; between5000 nits and 10000 nits, inclusive; or greater than 10000 nits.(EEE26.) The method as recited in enumerated example embodiment 17,further comprising converting one or more input images represented,received, transmitted, or stored with the reference encoded image datafrom an input video signal into one or more output images represented,received, transmitted, or stored with the device-specific image datacontained in an output video signal. (EEE27.) The method as recited inenumerated example embodiment 17, wherein the device-specific image datasupports image rendering in one of a high-resolution high dynamic range(HDR) image format, a RGB color space associated with the Academy ColorEncoding Specification (ACES) standard of the Academy of Motion PictureArts and Sciences (AMPAS), a P3 color space standard of the DigitalCinema Initiative, a Reference Input Medium Metric/Reference OutputMedium Metric (RIMM/ROMM) standard, an sRGB color space, or a RGB colorspace associated with the BT.709 Recommendation standard of theInternational Telecommunications Union (ITU). (EEE28.) The method asrecited in enumerated example embodiment 17, wherein the luminancedifference between the two reference gray levels represented by the twoadjacent reference digital code values is less than a just noticeabledifference threshold at the particular light level. (EEE29.) the methodas recited in enumerated example embodiment 17, wherein the particularlight level comprises a luminance value between the two luminancevalues, inclusive. (EEE30.) The method as recited in enumerated exampleembodiment 17, wherein the set of device-specific digital code valuescomprises integer values in a code space with a bit depth of: 8 bits;greater than 8 but less than 12 bits; or 12 bits or more. (EEE31.) Themethod as recited in enumerated example embodiment 17, wherein the setof device-specific gray levels comprises a set of quantized luminancevalues. (EEE32.) The method as recited in enumerated example embodiment17, wherein at least one of the reference mapping and thedevice-specific mapping is determined based at least in part on afunctional model represented with one or more functions. (EEE33.) Themethod as recited in enumerated example embodiment 32, wherein thefunctional model comprises one or more model parameters, and whereinvalues of the model parameters are optimized through minimizingdeviations between predicted code values and target code values.(EEE34.) An encoder performing any of the methods as recited inenumerated example embodiments 1-16, inclusive. (EEE35.) A decoderperforming any of the methods as recited in enumerated exampleembodiments 17-33, inclusive. (EEE36.) A system performing any of themethods as recited in enumerated example embodiments 1-33, inclusive.(EEE37.) A system, comprising: an encoder, which is configured to:receive image data to be encoded, encode, based on a reference mappingbetween a set of reference digital code values and a set of referencegray levels, the received image data into reference encoded image data,wherein luminance values in the image data to be encoded being arerepresented by the set of reference digital code values, wherein aluminance difference between two reference gray levels represented bytwo adjacent reference digital code values in the set of referencedigital code values is inversely proportional to a peak contrastsensitivity of human vision adapted at a particular light level; andoutput the reference encoded image data; and a decoder, which isconfigured to: determine a digital code mapping between the set ofreference digital code values and a set of device-specific digital codevalues, wherein the set of device-specific digital code values is mappedin a device-specific mapping to a set of device-specific gray levels;receive the reference encoded image data; and transcode, based on thedigital code mapping, the reference encoded image data encoded with theset of reference digital code values into device-specific image dataencoded with the set of device-specific digital control codes, whereinluminance values in the device-specific image data are based on the setof device-specific digital code values. (EEE38.) An image decoder,comprising: a mapping determiner, which determines a digital codemapping between a set of reference digital code values and a set ofdevice-specific digital code values, wherein the set of referencedigital code values is mapped in a reference mapping to a set ofreference gray levels, and wherein the set of device-specific digitalcode values is mapped in a device-specific mapping to a set ofdevice-specific gray levels; a receiver, which receives referenceencoded image data encoded with the set of reference digital codevalues, wherein luminance values in the reference encoded image data arebased on the set of reference digital code values, wherein a luminancedifference between two reference gray levels represented by two adjacentreference digital code values in the set of reference digital codevalues is inversely proportional to a peak contrast sensitivity of humanvision adapted at a particular light level; and a transcoder which,based on the digital code mapping, transforms the reference encodedimage data encoded with the set of reference digital code values intodevice-specific image data encoded with the set of device-specificdigital control codes, wherein luminance values in the device-specificimage data are based on the set of device-specific digital code values.(EEE39.) The decoder as recited in enumerated example embodiment 38,wherein the decoder is configured to: determine a set of correspondencerelationships between the set of reference digital code values and theset of device-specific digital code values, wherein a correspondencerelationship in the set of correspondence relationship relates areference digital code value in the set of reference digital code valuesto a device-specific digital code value; compare a first luminancedifference at the reference digital code value and a second luminancedifference at the device-specific digital code value; and store analgorithm flag, based on comparing the first luminance difference andthe second luminance difference, wherein the algorithm flag functions toflag whether dithering, decontouring, or no operation should beperformed for the reference digital code value. (EEE40.) The decoder asrecited in enumerated example embodiment 38, wherein the decoder isfurther configured to: determine a reference digital code value from thereference encoded image data for a pixel; and determine whether analgorithm flag is set for the reference digital code value. (EEE41.) Thedecoder as recited in enumerated example embodiment 40, wherein thedecoder is further configured to perform a decontour function on thepixel, in response to determining that an algorithm flag is set fordecontour. (EEE42.) The decoder as recited in enumerated exampleembodiment 40, wherein the decoder is further configured to perform adithering operation on the pixel, in response to determining that analgorithm flag is set for dithering. (EEE43.) The decoder as recited inenumerated example embodiment 38, wherein the decoder is furtherconfigured to: render one or more images on a display based on thedevice-specific image data encoded with the set of device-specificdigital control codes, the display comprising at least one of a visibledynamic range (VDR) display, a standard dynamic range (SDR) display, atablet computer display, or a handheld device display. (EEE44.) Thedecoder as recited in enumerated example embodiment 38, wherein adevice-specific gray scale display function (GSDF) specifies thedevice-specific mapping between the set of device-specific digital codevalues and the set of device-specific gray levels. (EEE45.) The decoderas recited in enumerated example embodiment 38, wherein thedevice-specific mapping is derived based on one or more displayparameters and zero or more viewing condition parameters. (EEE46.) Thedecoder as recited in enumerated example embodiment 38, wherein the setof device-specific gray levels spans (e.g., covers) a dynamic range withan upper limit having a value of: less than 100 nits; no less than 100nits but less than 500 nits; between 500 nits and 1000 nits, inclusive;between 1000 and 5000 nits, inclusive; between 5000 nits and 10000 nits,inclusive; or greater than 10000 nits. (EEE47.) The decoder as recitedin enumerated example embodiment 38, further comprising a converter forconverting one or more input images represented, received, transmitted,or stored with the reference encoded image data from an input videosignal into one or more output images represented, received,transmitted, or stored with the device-specific image data contained inan output video signal. (EEE48.) The decoder as recited in enumeratedexample embodiment 38, wherein the device-specific image data supportsimage rendering in one of a high-resolution high dynamic range (HDR)image format, a RGB color space associated with the Academy ColorEncoding Specification (ACES) standard of the Academy of Motion PictureArts and Sciences (AMPAS), a P3 color space standard of the DigitalCinema Initiative, a Reference Input Medium Metric/Reference OutputMedium Metric (RIMM/ROMM) standard, an sRGB color space, or a RGB colorspace associated with the BT.709 Recommendation standard of theInternational Telecommunications Union (ITU). (EEE49.) The decoder asrecited in enumerated example embodiment 38, wherein the luminancedifference between the two reference gray levels represented by the twoadjacent reference digital code values is less than a just noticeabledifference (JND) threshold at the particular light level. (EEE50.) Thedecoder as recited in enumerated example embodiment 38, wherein theparticular light level comprises a luminance value that lies between thetwo luminance values, inclusive. (EEE51.) The decoder as recited inenumerated example embodiment 38, wherein the set of device-specificdigital code values comprises integer values in a code space with a bitdepth of: 8 bits; greater than 8 but less than 12 bits; or 12 bits ormore. (EEE52.) The decoder as recited in enumerated example embodiment31, wherein the set of device-specific gray levels comprises a set ofquantized luminance values. (EEE53.) The decoder as recited inenumerated example embodiment 38, wherein at least one of the referencemapping and the device-specific mapping is determined based at least inpart on a functional model represented with one or more functions.(EEE54.) The decoder as recited in enumerated example embodiment 53,wherein the functional model comprises one or more model parameters, andwherein values of the model parameters are optimized through minimizingdeviations between predicted code values and target code values.(EEE55.) A non-transitory computer readable storage medium comprisinginstructions that are encoded and stored therewith, which when executedwith a computer or a processor thereof, cause, control or program thecomputer or the processor to execute, perform or control a process, theprocess for decoding an image, the image decoding process comprising thestep of: determining a digital code mapping between a set of referencedigital code values and a set of device-specific digital code values,wherein the set of reference digital code values is mapped in areference mapping to a set of reference gray levels, and wherein the setof device-specific digital code values is mapped in a device-specificmapping to a set of device-specific gray levels; receiving referenceencoded image data encoded with the set of reference digital codevalues, wherein luminance values in the reference encoded image data arebased on the set of reference digital code values, wherein a luminancedifference between two reference gray levels represented by two adjacentreference digital code values in the set of reference digital codevalues is inversely proportional to a peak contrast sensitivity of humanvision adapted at a particular light level; and transcoding, based onthe digital code mapping, the reference encoded image data encoded withthe set of reference digital code values into device-specific image dataencoded with the set of device-specific digital control codes, whereinluminance. (EEE56.) An image decoding system, comprising: means fordetermining a digital code mapping between a set of reference digitalcode values and a set of device-specific digital code values, whereinthe set of reference digital code values is mapped in a referencemapping to a set of reference gray levels, and wherein the set ofdevice-specific digital code values is mapped in a device-specificmapping to a set of device-specific gray levels; means for receivingreference encoded image data encoded with the set of reference digitalcode values, wherein luminance values in the reference encoded imagedata are based on the set of reference digital code values, wherein aluminance difference between two reference gray levels represented bytwo adjacent reference digital code values in the set of referencedigital code values is inversely proportional to a peak contrastsensitivity of human vision adapted at a particular light level; andmeans for transcoding, based on the digital code mapping, the referenceencoded image data encoded with the set of reference digital code valuesinto device-specific image data encoded with the set of device-specificdigital control codes, wherein luminance values in the device-specificimage data are based on the set of device-specific digital code values.(EEE57.) A method, comprising the steps of: receiving reference encodedimage data encoded with reference code values, the reference code valuesrepresenting a set of reference gray levels, a first pair of neighboringgray levels in the set of gray levels relating to a first peak contrastsensitivity of human vision adapted at a first light level, and a secondpair of neighboring gray levels in the set of gray levels relating to asecond peak contrast sensitivity of human vision adapted at a seconddifferent light level; accessing a code mapping between reference codevalues and device-specific code values, the device-specific code valuesrepresenting a set of device-specific gray levels; and transcoding,based on the code mapping, the reference encoded image data intodevice-specific image data encoded with the device-specific controlcodes. (EEE58.) The method as recited in enumerated example embodiment57, wherein the set of reference gray levels covers a dynamic range withan upper limit having a value of: less than 500 nits; between 500 nitsand 1000 nits, inclusive; between 1000 and 5000 nits, inclusive; between5000 nits and 10000 nits, inclusive; between 10000 nits and 15000 nits,inclusive, or greater than 15000 nits. (EEE59.) The method as recited inenumerated example embodiment 57, wherein the set of reference graylevels is configured based on a human vision model that supports a fieldof view of greater than 40 degrees. (EEE60.) The method as recited inenumerated example embodiment 57, wherein the set of reference graylevels relates to variable spatial frequencies below a cut-off spatialfrequency. (EEE61.) The method as recited in enumerated exampleembodiment 57, wherein the code mapping is configured to evenlydistribute perceptually noticeable errors in a dynamic range covered bythe device-specific gray levels. (EEE62.) The method as recited inenumerated example embodiment 57, wherein a first luminance valuedifference of the first pair of neighboring gray levels in the set ofgray levels relates to the first peak contrast sensitivity inverselywith a multiplicative constant, and wherein a second luminance valuedifference of the second pair of neighboring gray levels relates to thesecond peak contrast sensitivity inversely with the same multiplicativeconstant. (EEE63.) The method as recited in enumerated exampleembodiment 57, wherein a reference code value in the reference codevalues and a reference gray level represented by the reference codevalue have different numeric values. (EEE64.) The method as recited inenumerated example embodiment 57, wherein transcoding, based on the codemapping, the reference encoded image data into device-specific imagedata encoded with the device-specific control codes includes:determining a first luminance value difference between two adjacentreference code values at a reference code value; determining a secondluminance value difference between two adjacent device-specific codevalues at a device-specific code value, wherein the device-specific codevalue corresponds to the reference code value; and apply, based on acomparison of the first luminance value difference and the secondluminance value difference, one of a dithering algorithm or adecontouring algorithm to at least one pixel in the device-specificimage data. (EEE65.) A imaging device comprising: a data receiverconfigured to receive reference encoded image data comprising referencecode values, the reference encoded image data being encoded by anexternal coding system, the reference code values representing referencegray levels, the reference gray levels being selected using a referencegrayscale display function based on perceptual non-linearity of humanvision adapted at different light levels to spatial frequencies; a dataconverter configured to access a code mapping between the reference codevalues and device-specific code values of the imaging device, thedevice-specific code values configured to produce device-specific graylevels configured for the imaging device, the data converter beingconfigured to transcode, based on the code mapping, the referenceencoded image data into device-specific image data encoded with thedevice-specific code values, wherein the imaging device is at least oneof a: game machine, television, laptop computer, desktop computer,netbook computer, computer workstation, cellular radiotelephone,electronic book reader, point of sale terminal, and computer kiosk.

The following Table 3 describes the calculation of the Perceptual CurveEOTF for converting digital video code values into absolute linearluminance levels at the point of display. Also included is the inverseOETF calculation for converting absolute linear luminance into digitalcode values.

TABLE 3 Exemplary Specification for Perceptual Curve EOTF Exemplary EOTFDecode Equations:$V = \frac{D - {4 \cdot 2^{b - 10}}}{1015 \cdot 2^{b - 10}}$$Y = \left( \frac{\max\left\lbrack {\left( {V^{1/m} - c_{1}} \right),0} \right\rbrack}{c_{2} - {c_{3}V^{1/m}}} \right)^{1/n}$L = 10,000 · Y Exemplary OETF Encode Equations:$Y = \frac{L}{10\text{,}000}$$V = \left( \frac{c_{1} + {c_{2}Y^{n}}}{1 + {c_{3}Y^{n}}} \right)^{m}$ D= INT(1015 · V · 2^(b−10)) + 4 · 2^(b−10) Exemplary Constants:$n = {{\frac{2610}{4096} \times \frac{1}{4}} \approx 0.15930176}$$m = {{\frac{2523}{4096} \times 128} = 78.84375}$$c_{1} = {{c_{3} - c_{2} + 1} = {\frac{3424}{4096} = 0.8359375}}$$c_{2} = {{\frac{2413}{4096} \times 32} = 18.8515625}$$c_{3} = {{\frac{2392}{4096} \times 32} = 18.6875}$ Exemplary EquationDefinitions: D = Perceptual Curve digital code value, SDI-legal unsignedinteger, 10 or 12 bits b = number of bits per component in digitalsignal representation, 10 or 12 V = normalized Perceptual Curve signalvalue, 0 ≦ V ≦ 1 Y = normalized luminance value, 0 ≦ Y ≦ 1 L = absoluteluminance value, 0 ≦ L ≦ 10,000 cd/m² Notes: 1. The operator INT returnsthe value of 0 for fractional parts in the range of 0 to 0.4999 . . .and +1 for fractional parts in the range of 0.5 to 0.9999 . . . , i.e.it rounds up fractions above 0.5. 2. All constants are defined as exactmultiples of 12 bit rationals to avoid rounding concerns. 3. R, G, or Bsignal components are to be computed in the same way as the Y signalcomponent described above.

The following Table 4 shows exemplary values for 10 bits.

TABLE 4 Exemplary Table of Values for 10 bits D V Y L (cd/m²) 0 Reserved1 Reserved 2 Reserved 3 Reserved 4 0.00000 0.000E+00 0.00000 5 0.000994.096E−09 0.00004 6 0.00197 1.329E−08 0.00013 7 0.00296 2.659E−080.00027 8 0.00394 4.374E−08 0.00044 9 0.00493 6.463E−08 0.00065 100.00591 8.922E−08 0.00089 11 0.00690 1.175E−07 0.00117 12 0.007881.495E−07 0.00149 13 0.00887 1.852E−07 0.00185 14 0.00985 2.248E−070.00225 15 0.01084 2.681E−07 0.00268 16 0.01182 3.154E−07 0.00315 170.01281 3.666E−07 0.00367 18 0.01379 4.219E−07 0.00422 19 0.014784.812E−07 0.00481 20 0.01576 5.447E−07 0.00545 21 0.01675 6.125E−070.00613 22 0.01773 6.846E−07 0.00685 23 0.01872 7.610E−07 0.00761 240.01970 8.420E−07 0.00842 25 0.02069 9.275E−07 0.00927 26 0.021671.018E−06 0.01018 27 0.02266 1.112E−06 0.01112 28 0.02365 1.212E−060.01212 29 0.02463 1.317E−06 0.01317 30 0.02562 1.426E−06 0.01426 310.02660 1.541E−06 0.01541 32 0.02759 1.661E−06 0.01661 33 0.028571.786E−06 0.01786 34 0.02956 1.916E−06 0.01916 35 0.03054 2.052E−060.02052 36 0.03153 2.193E−06 0.02193 37 0.03251 2.340E−06 0.02340 380.03350 2.493E−06 0.02493 39 0.03448 2.652E−06 0.02652 40 0.035472.816E−06 0.02816 41 0.03645 2.987E−06 0.02987 42 0.03744 3.163E−060.03163 43 0.03842 3.346E−06 0.03346 44 0.03941 3.536E−06 0.03536 450.04039 3.731E−06 0.03731 46 0.04138 3.934E−06 0.03934 47 0.042364.143E−06 0.04143 48 0.04335 4.358E−06 0.04358 49 0.04433 4.581E−060.04581 50 0.04532 4.810E−06 0.04810 51 0.04631 5.047E−06 0.05047 520.04729 5.291E−06 0.05291 53 0.04828 5.542E−06 0.05542 54 0.049265.801E−06 0.05801 55 0.05025 6.067E−06 0.06067 56 0.05123 6.341E−060.06341 57 0.05222 6.623E−06 0.06623 58 0.05320 6.913E−06 0.06913 590.05419 7.211E−06 0.07211 60 0.05517 7.517E−06 0.07517 61 0.056167.831E−06 0.07831 62 0.05714 8.154E−06 0.08154 63 0.05813 8.485E−060.08485 64 0.05911 8.825E−06 0.08825 65 0.06010 9.174E−06 0.09174 660.06108 9.532E−06 0.09532 67 0.06207 9.899E−06 0.09899 68 0.063051.027E−05 0.10275 69 0.06404 1.066E−05 0.10660 70 0.06502 1.106E−050.11055 71 0.06601 1.146E−05 0.11460 72 0.06700 1.187E−05 0.11874 730.06798 1.230E−05 0.12298 74 0.06897 1.273E−05 0.12733 75 0.069951.318E−05 0.13177 76 0.07094 1.363E−05 0.13632 77 0.07192 1.410E−050.14097 78 0.07291 1.457E−05 0.14573 79 0.07389 1.506E−05 0.15060 800.07488 1.556E−05 0.15558 81 0.07586 1.607E−05 0.16067 82 0.076851.659E−05 0.16587 83 0.07783 1.712E−05 0.17119 84 0.07882 1.766E−050.17662 85 0.07980 1.822E−05 0.18217 86 0.08079 1.878E−05 0.18783 870.08177 1.936E−05 0.19362 88 0.08276 1.995E−05 0.19953 89 0.083742.056E−05 0.20556 90 0.08473 2.117E−05 0.21172 91 0.08571 2.180E−050.21801 92 0.08670 2.244E−05 0.22443 93 0.08768 2.310E−05 0.23097 940.08867 2.377E−05 0.23765 95 0.08966 2.445E−05 0.24447 96 0.090642.514E−05 0.25142 97 0.09163 2.585E−05 0.25850 98 0.09261 2.657E−050.26573 99 0.09360 2.731E−05 0.27310 100 0.09458 2.806E−05 0.28061 1010.09557 2.883E−05 0.28826 102 0.09655 2.961E−05 0.29607 103 0.097543.040E−05 0.30402 104 0.09852 3.121E−05 0.31212 105 0.09951 3.204E−050.32038 106 0.10049 3.288E−05 0.32879 107 0.10148 3.374E−05 0.33736 1080.10246 3.461E−05 0.34608 109 0.10345 3.550E−05 0.35497 110 0.104433.640E−05 0.36402 111 0.10542 3.732E−05 0.37324 112 0.10640 3.826E−050.38262 113 0.10739 3.922E−05 0.39217 114 0.10837 4.019E−05 0.40189 1150.10936 4.118E−05 0.41179 116 0.11034 4.219E−05 0.42186 117 0.111334.321E−05 0.43211 118 0.11232 4.425E−05 0.44254 119 0.11330 4.531E−050.45315 120 0.11429 4.639E−05 0.46394 121 0.11527 4.749E−05 0.47492 1220.11626 4.861E−05 0.48609 123 0.11724 4.975E−05 0.49746 124 0.118235.090E−05 0.50901 125 0.11921 5.208E−05 0.52076 126 0.12020 5.327E−050.53271 127 0.12118 5.449E−05 0.54486 128 0.12217 5.572E−05 0.55722 1290.12315 5.698E−05 0.56978 130 0.12414 5.825E−05 0.58255 131 0.125125.955E−05 0.59552 132 0.12611 6.087E−05 0.60872 133 0.12709 6.221E−050.62212 134 0.12808 6.357E−05 0.63575 135 0.12906 6.496E−05 0.64959 1360.13005 6.637E−05 0.66366 137 0.13103 6.780E−05 0.67796 138 0.132026.925E−05 0.69248 139 0.13300 7.072E−05 0.70724 140 0.13399 7.222E−050.72223 141 0.13498 7.375E−05 0.73746 142 0.13596 7.529E−05 0.75292 1430.13695 7.686E−05 0.76863 144 0.13793 7.846E−05 0.78458 145 0.138928.008E−05 0.80079 146 0.13990 8.172E−05 0.81724 147 0.14089 8.339E−050.83395 148 0.14187 8.509E−05 0.85091 149 0.14286 8.681E−05 0.86814 1500.14384 8.856E−05 0.88562 151 0.14483 9.034E−05 0.90338 152 0.145819.214E−05 0.92140 153 0.14680 9.397E−05 0.93969 154 0.14778 9.583E−050.95826 155 0.14877 9.771E−05 0.97711 156 0.14975 9.962E−05 0.99624 1570.15074 1.016E−04 1.01565 158 0.15172 1.035E−04 1.03535 159 0.152711.055E−04 1.05534 160 0.15369 1.076E−04 1.07563 161 0.15468 1.096E−041.09622 162 0.15567 1.117E−04 1.11710 163 0.15665 1.138E−04 1.13829 1640.15764 1.160E−04 1.15979 165 0.15862 1.182E−04 1.18160 166 0.159611.204E−04 1.20372 167 0.16059 1.226E−04 1.22616 168 0.16158 1.249E−041.24892 169 0.16256 1.272E−04 1.27201 170 0.16355 1.295E−04 1.29543 1710.16453 1.319E−04 1.31918 172 0.16552 1.343E−04 1.34326 173 0.166501.368E−04 1.36769 174 0.16749 1.392E−04 1.39246 175 0.16847 1.418E−041.41758 176 0.16946 1.443E−04 1.44304 177 0.17044 1.469E−04 1.46887 1780.17143 1.495E−04 1.49505 179 0.17241 1.522E−04 1.52160 180 0.173401.549E−04 1.54851 181 0.17438 1.576E−04 1.57579 182 0.17537 1.603E−041.60345 183 0.17635 1.631E−04 1.63148 184 0.17734 1.660E−04 1.65990 1850.17833 1.689E−04 1.68871 186 0.17931 1.718E−04 1.71791 187 0.180301.748E−04 1.74750 188 0.18128 1.777E−04 1.77749 189 0.18227 1.808E−041.80789 190 0.18325 1.839E−04 1.83870 191 0.18424 1.870E−04 1.86991 1920.18522 1.902E−04 1.90155 193 0.18621 1.934E−04 1.93361 194 0.187191.966E−04 1.96609 195 0.18818 1.999E−04 1.99900 196 0.18916 2.032E−042.03235 197 0.19015 2.066E−04 2.06614 198 0.19113 2.100E−04 2.10037 1990.19212 2.135E−04 2.13506 200 0.19310 2.170E−04 2.17019 201 0.194092.206E−04 2.20579 202 0.19507 2.242E−04 2.24185 203 0.19606 2.278E−042.27837 204 0.19704 2.315E−04 2.31537 205 0.19803 2.353E−04 2.35285 2060.19901 2.391E−04 2.39081 207 0.20000 2.429E−04 2.42926 208 0.200992.468E−04 2.46821 209 0.20197 2.508E−04 2.50765 210 0.20296 2.548E−042.54760 211 0.20394 2.588E−04 2.58805 212 0.20493 2.629E−04 2.62902 2130.20591 2.671E−04 2.67051 214 0.20690 2.713E−04 2.71252 215 0.207882.755E−04 2.75507 216 0.20887 2.798E−04 2.79815 217 0.20985 2.842E−042.84177 218 0.21084 2.886E−04 2.88594 219 0.21182 2.931E−04 2.93066 2200.21281 2.976E−04 2.97594 221 0.21379 3.022E−04 3.02179 222 0.214783.068E−04 3.06820 223 0.21576 3.115E−04 3.11519 224 0.21675 3.163E−043.16276 225 0.21773 3.211E−04 3.21092 226 0.21872 3.260E−04 3.25967 2270.21970 3.309E−04 3.30903 228 0.22069 3.359E−04 3.35898 229 0.221673.410E−04 3.40955 230 0.22266 3.461E−04 3.46074 231 0.22365 3.513E−043.51255 232 0.22463 3.565E−04 3.56500 233 0.22562 3.618E−04 3.61808 2340.22660 3.672E−04 3.67180 235 0.22759 3.726E−04 3.72618 236 0.228573.781E−04 3.78121 237 0.22956 3.837E−04 3.83690 238 0.23054 3.893E−043.89327 239 0.23153 3.950E−04 3.95031 240 0.23251 4.008E−04 4.00803 2410.23350 4.066E−04 4.06645 242 0.23448 4.126E−04 4.12556 243 0.235474.185E−04 4.18537 244 0.23645 4.246E−04 4.24590 245 0.23744 4.307E−044.30715 246 0.23842 4.369E−04 4.36912 247 0.23941 4.432E−04 4.43182 2480.24039 4.495E−04 4.49527 249 0.24138 4.559E−04 4.55946 250 0.242364.624E−04 4.62440 251 0.24335 4.690E−04 4.69011 252 0.24433 4.757E−044.75659 253 0.24532 4.824E−04 4.82385 254 0.24631 4.892E−04 4.89189 2550.24729 4.961E−04 4.96073 256 0.24828 5.030E−04 5.03036 257 0.249265.101E−04 5.10081 258 0.25025 5.172E−04 5.17207 259 0.25123 5.244E−045.24416 260 0.25222 5.317E−04 5.31707 261 0.25320 5.391E−04 5.39084 2620.25419 5.465E−04 5.46545 263 0.25517 5.541E−04 5.54091 264 0.256165.617E−04 5.61725 265 0.25714 5.694E−04 5.69446 266 0.25813 5.773E−045.77255 267 0.25911 5.852E−04 5.85153 268 0.26010 5.931E−04 5.93142 2690.26108 6.012E−04 6.01221 270 0.26207 6.094E−04 6.09393 271 0.263056.177E−04 6.17657 272 0.26404 6.260E−04 6.26014 273 0.26502 6.345E−046.34467 274 0.26601 6.430E−04 6.43014 275 0.26700 6.517E−04 6.51658 2760.26798 6.604E−04 6.60400 277 0.26897 6.692E−04 6.69239 278 0.269956.782E−04 6.78178 279 0.27094 6.872E−04 6.87217 280 0.27192 6.964E−046.96357 281 0.27291 7.056E−04 7.05600 282 0.27389 7.149E−04 7.14945 2830.27488 7.244E−04 7.24395 284 0.27586 7.339E−04 7.33949 285 0.276857.436E−04 7.43610 286 0.27783 7.534E−04 7.53378 287 0.27882 7.633E−047.63254 288 0.27980 7.732E−04 7.73240 289 0.28079 7.833E−04 7.83335 2900.28177 7.935E−04 7.93542 291 0.28276 8.039E−04 8.03862 292 0.283748.143E−04 8.14295 293 0.28473 8.248E−04 8.24842 294 0.28571 8.355E−048.35505 295 0.28670 8.463E−04 8.46285 296 0.28768 8.572E−04 8.57183 2970.28867 8.682E−04 8.68200 298 0.28966 8.793E−04 8.79337 299 0.290648.906E−04 8.90595 300 0.29163 9.020E−04 9.01976 301 0.29261 9.135E−049.13480 302 0.29360 9.251E−04 9.25109 303 0.29458 9.369E−04 9.36864 3040.29557 9.487E−04 9.48746 305 0.29655 9.608E−04 9.60757 306 0.297549.729E−04 9.72897 307 0.29852 9.852E−04 9.85168 308 0.29951 9.976E−049.97571 309 0.30049 1.010E−03 10.10108 310 0.30148 1.023E−03 10.22779311 0.30246 1.036E−03 10.35585 312 0.30345 1.049E−03 10.48529 3130.30443 1.062E−03 10.61612 314 0.30542 1.075E−03 10.74834 315 0.306401.088E−03 10.88197 316 0.30739 1.102E−03 11.01703 317 0.30837 1.115E−0311.15352 318 0.30936 1.129E−03 11.29147 319 0.31034 1.143E−03 11.43087320 0.31133 1.157E−03 11.57176 321 0.31232 1.171E−03 11.71414 3220.31330 1.186E−03 11.85803 323 0.31429 1.200E−03 12.00343 324 0.315271.215E−03 12.15037 325 0.31626 1.230E−03 12.29886 326 0.31724 1.245E−0312.44891 327 0.31823 1.260E−03 12.60054 328 0.31921 1.275E−03 12.75376329 0.32020 1.291E−03 12.90859 330 0.32118 1.307E−03 13.06505 3310.32217 1.322E−03 13.22314 332 0.32315 1.338E−03 13.38288 333 0.324141.354E−03 13.54430 334 0.32512 1.371E−03 13.70739 335 0.32611 1.387E−0313.87219 336 0.32709 1.404E−03 14.03870 337 0.32808 1.421E−03 14.20695338 0.32906 1.438E−03 14.37694 339 0.33005 1.455E−03 14.54869 3400.33103 1.472E−03 14.72223 341 0.33202 1.490E−03 14.89756 342 0.333001.507E−03 15.07471 343 0.33399 1.525E−03 15.25369 344 0.33498 1.543E−0315.43451 345 0.33596 1.562E−03 15.61720 346 0.33695 1.580E−03 15.80177347 0.33793 1.599E−03 15.98824 348 0.33892 1.618E−03 16.17663 3490.33990 1.637E−03 16.36695 350 0.34089 1.656E−03 16.55922 351 0.341871.675E−03 16.75346 352 0.34286 1.695E−03 16.94970 353 0.34384 1.715E−0317.14794 354 0.34483 1.735E−03 17.34820 355 0.34581 1.755E−03 17.55051356 0.34680 1.775E−03 17.75488 357 0.34778 1.796E−03 17.96133 3580.34877 1.817E−03 18.16989 359 0.34975 1.838E−03 18.38056 360 0.350741.859E−03 18.59338 361 0.35172 1.881E−03 18.80835 362 0.35271 1.903E−0319.02551 363 0.35369 1.924E−03 19.24486 364 0.35468 1.947E−03 19.46644365 0.35567 1.969E−03 19.69025 366 0.35665 1.992E−03 19.91632 3670.35764 2.014E−03 20.14468 368 0.35862 2.038E−03 20.37534 369 0.359612.061E−03 20.60832 370 0.36059 2.084E−03 20.84364 371 0.36158 2.108E−0321.08134 372 0.36256 2.132E−03 21.32141 373 0.36355 2.156E−03 21.56390374 0.36453 2.181E−03 21.80882 375 0.36552 2.206E−03 22.05620 3760.36650 2.231E−03 22.30605 377 0.36749 2.256E−03 22.55840 378 0.368472.281E−03 22.81327 379 0.36946 2.307E−03 23.07068 380 0.37044 2.333E−0323.33067 381 0.37143 2.359E−03 23.59324 382 0.37241 2.386E−03 23.85843383 0.37340 2.413E−03 24.12626 384 0.37438 2.440E−03 24.39674 3850.37537 2.467E−03 24.66992 386 0.37635 2.495E−03 24.94581 387 0.377342.522E−03 25.22443 388 0.37833 2.551E−03 25.50582 389 0.37931 2.579E−0325.78999 390 0.38030 2.608E−03 26.07697 391 0.38128 2.637E−03 26.36679392 0.38227 2.666E−03 26.65947 393 0.38325 2.696E−03 26.95504 3940.38424 2.725E−03 27.25352 395 0.38522 2.755E−03 27.55495 396 0.386212.786E−03 27.85934 397 0.38719 2.817E−03 28.16672 398 0.38818 2.848E−0328.47713 399 0.38916 2.879E−03 28.79059 400 0.39015 2.911E−03 29.10712401 0.39113 2.943E−03 29.42676 402 0.39212 2.975E−03 29.74953 4030.39310 3.008E−03 30.07546 404 0.39409 3.040E−03 30.40459 405 0.395073.074E−03 30.73692 406 0.39606 3.107E−03 31.07251 407 0.39704 3.141E−0331.41137 408 0.39803 3.175E−03 31.75354 409 0.39901 3.210E−03 32.09905410 0.40000 3.245E−03 32.44792 411 0.40099 3.280E−03 32.80018 4120.40197 3.316E−03 33.15588 413 0.40296 3.352E−03 33.51503 414 0.403943.388E−03 33.87767 415 0.40493 3.424E−03 34.24383 416 0.40591 3.461E−0334.61355 417 0.40690 3.499E−03 34.98684 418 0.40788 3.536E−03 35.36376419 0.40887 3.574E−03 35.74432 420 0.40985 3.613E−03 36.12857 4210.41084 3.652E−03 36.51652 422 0.41182 3.691E−03 36.90823 423 0.412813.730E−03 37.30372 424 0.41379 3.770E−03 37.70303 425 0.41478 3.811E−0338.10618 426 0.41576 3.851E−03 38.51322 427 0.41675 3.892E−03 38.92418428 0.41773 3.934E−03 39.33909 429 0.41872 3.976E−03 39.75800 4300.41970 4.018E−03 40.18093 431 0.42069 4.061E−03 40.60792 432 0.421674.104E−03 41.03901 433 0.42266 4.147E−03 41.47423 434 0.42365 4.191E−0341.91363 435 0.42463 4.236E−03 42.35723 436 0.42562 4.281E−03 42.80509437 0.42660 4.326E−03 43.25723 438 0.42759 4.371E−03 43.71369 4390.42857 4.417E−03 44.17451 440 0.42956 4.464E−03 44.63974 441 0.430544.511E−03 45.10941 442 0.43153 4.558E−03 45.58355 443 0.43251 4.606E−0346.06222 444 0.43350 4.655E−03 46.54545 445 0.43448 4.703E−03 47.03328446 0.43547 4.753E−03 47.52575 447 0.43645 4.802E−03 48.02291 4480.43744 4.852E−03 48.52479 449 0.43842 4.903E−03 49.03144 450 0.439414.954E−03 49.54290 451 0.44039 5.006E−03 50.05921 452 0.44138 5.058E−0350.58042 453 0.44236 5.111E−03 51.10657 454 0.44335 5.164E−03 51.63771455 0.44433 5.217E−03 52.17387 456 0.44532 5.272E−03 52.71511 4570.44631 5.326E−03 53.26147 458 0.44729 5.381E−03 53.81299 459 0.448285.437E−03 54.36973 460 0.44926 5.493E−03 54.93172 461 0.45025 5.550E−0355.49901 462 0.45123 5.607E−03 56.07166 463 0.45222 5.665E−03 56.64970464 0.45320 5.723E−03 57.23319 465 0.45419 5.782E−03 57.82218 4660.45517 5.842E−03 58.41671 467 0.45616 5.902E−03 59.01683 468 0.457145.962E−03 59.62260 469 0.45813 6.023E−03 60.23406 470 0.45911 6.085E−0360.85126 471 0.46010 6.147E−03 61.47426 472 0.46108 6.210E−03 62.10311473 0.46207 6.274E−03 62.73785 474 0.46305 6.338E−03 63.37855 4750.46404 6.403E−03 64.02525 476 0.46502 6.468E−03 64.67801 477 0.466016.534E−03 65.33688 478 0.46700 6.600E−03 66.00191 479 0.46798 6.667E−0366.67316 480 0.46897 6.735E−03 67.35069 481 0.46995 6.803E−03 68.03455482 0.47094 6.872E−03 68.72480 483 0.47192 6.942E−03 69.42149 4840.47291 7.012E−03 70.12468 485 0.47389 7.083E−03 70.83443 486 0.474887.155E−03 71.55079 487 0.47586 7.227E−03 72.27383 488 0.47685 7.300E−0373.00361 489 0.47783 7.374E−03 73.74018 490 0.47882 7.448E−03 74.48361491 0.47980 7.523E−03 75.23395 492 0.48079 7.599E−03 75.99127 4930.48177 7.676E−03 76.75562 494 0.48276 7.753E−03 77.52708 495 0.483747.831E−03 78.30570 496 0.48473 7.909E−03 79.09155 497 0.48571 7.988E−0379.88469 498 0.48670 8.069E−03 80.68519 499 0.48768 8.149E−03 81.49310500 0.48867 8.231E−03 82.30851 501 0.48966 8.313E−03 83.13146 5020.49064 8.396E−03 83.96204 503 0.49163 8.480E−03 84.80031 504 0.492618.565E−03 85.64633 505 0.49360 8.650E−03 86.50017 506 0.49458 8.736E−0387.36191 507 0.49557 8.823E−03 88.23161 508 0.49655 8.911E−03 89.10934509 0.49754 9.000E−03 89.99518 510 0.49852 9.089E−03 90.88920 5110.49951 9.179E−03 91.79146 512 0.50049 9.270E−03 92.70205 513 0.501489.362E−03 93.62103 514 0.50246 9.455E−03 94.54848 515 0.50345 9.548E−0395.48448 516 0.50443 9.643E−03 96.42909 517 0.50542 9.738E−03 97.38241518 0.50640 9.834E−03 98.34449 519 0.50739 9.932E−03 99.31543 5200.50837 1.003E−02 100.29530 521 0.50936 1.013E−02 101.28417 522 0.510341.023E−02 102.28213 523 0.51133 1.033E−02 103.28927 524 0.512321.043E−02 104.30565 525 0.51330 1.053E−02 105.33136 526 0.514291.064E−02 106.36648 527 0.51527 1.074E−02 107.41110 528 0.516261.085E−02 108.46530 529 0.51724 1.095E−02 109.52917 530 0.518231.106E−02 110.60279 531 0.51921 1.117E−02 111.68624 532 0.520201.128E−02 112.77962 533 0.52118 1.139E−02 113.88301 534 0.522171.150E−02 114.99650 535 0.52315 1.161E−02 116.12018 536 0.524141.173E−02 117.25414 537 0.52512 1.184E−02 118.39847 538 0.526111.196E−02 119.55326 539 0.52709 1.207E−02 120.71860 540 0.528081.219E−02 121.89459 541 0.52906 1.231E−02 123.08132 542 0.530051.243E−02 124.27889 543 0.53103 1.255E−02 125.48739 544 0.532021.267E−02 126.70692 545 0.53300 1.279E−02 127.93758 546 0.533991.292E−02 129.17946 547 0.53498 1.304E−02 130.43266 548 0.535961.317E−02 131.69729 549 0.53695 1.330E−02 132.97344 550 0.537931.343E−02 134.26122 551 0.53892 1.356E−02 135.56073 552 0.539901.369E−02 136.87207 553 0.54089 1.382E−02 138.19535 554 0.541871.395E−02 139.53067 555 0.54286 1.409E−02 140.87814 556 0.543841.422E−02 142.23786 557 0.54483 1.436E−02 143.60995 558 0.545811.450E−02 144.99451 559 0.54680 1.464E−02 146.39166 560 0.547781.478E−02 147.80150 561 0.54877 1.492E−02 149.22415 562 0.549751.507E−02 150.65972 563 0.55074 1.521E−02 152.10833 564 0.551721.536E−02 153.57009 565 0.55271 1.550E−02 155.04511 566 0.553691.565E−02 156.53351 567 0.55468 1.580E−02 158.03542 568 0.555671.596E−02 159.55094 569 0.55665 1.611E−02 161.08021 570 0.557641.626E−02 162.62334 571 0.55862 1.642E−02 164.18046 572 0.559611.658E−02 165.75168 573 0.56059 1.673E−02 167.33714 574 0.561581.689E−02 168.93696 575 0.56256 1.706E−02 170.55126 576 0.563551.722E−02 172.18018 577 0.56453 1.738E−02 173.82384 578 0.565521.755E−02 175.48237 579 0.56650 1.772E−02 177.15591 580 0.567491.788E−02 178.84459 581 0.56847 1.805E−02 180.54854 582 0.569461.823E−02 182.26789 583 0.57044 1.840E−02 184.00279 584 0.571431.858E−02 185.75337 585 0.57241 1.875E−02 187.51977 586 0.573401.893E−02 189.30212 587 0.57438 1.911E−02 191.10058 588 0.575371.929E−02 192.91528 589 0.57635 1.947E−02 194.74636 590 0.577341.966E−02 196.59398 591 0.57833 1.985E−02 198.45827 592 0.579312.003E−02 200.33939 593 0.58030 2.022E−02 202.23748 594 0.581282.042E−02 204.15270 595 0.58227 2.061E−02 206.08519 596 0.583252.080E−02 208.03511 597 0.58424 2.100E−02 210.00261 598 0.585222.120E−02 211.98785 599 0.58621 2.140E−02 213.99098 600 0.587192.160E−02 216.01217 601 0.58818 2.181E−02 218.05157 602 0.589162.201E−02 220.10935 603 0.59015 2.222E−02 222.18566 604 0.591132.243E−02 224.28067 605 0.59212 2.264E−02 226.39455 606 0.593102.285E−02 228.52747 607 0.59409 2.307E−02 230.67959 608 0.595072.329E−02 232.85108 609 0.59606 2.350E−02 235.04212 610 0.597042.373E−02 237.25287 611 0.59803 2.395E−02 239.48352 612 0.599012.417E−02 241.73423 613 0.60000 2.440E−02 244.00519 614 0.600992.463E−02 246.29658 615 0.60197 2.486E−02 248.60857 616 0.602962.509E−02 250.94136 617 0.60394 2.533E−02 253.29512 618 0.604932.557E−02 255.67004 619 0.60591 2.581E−02 258.06630 620 0.606902.605E−02 260.48411 621 0.60788 2.629E−02 262.92364 622 0.608872.654E−02 265.38509 623 0.60985 2.679E−02 257.86866 624 0.610842.704E−02 270.37454 625 0.61182 2.729E−02 272.90293 626 0.612812.755E−02 275.45403 627 0.61379 2.780E−02 278.02804 628 0.614782.806E−02 280.62516 629 0.61576 2.832E−02 283.24561 630 0.616752.859E−02 285.88958 631 0.61773 2.886E−02 288.55729 632 0.618722.912E−02 291.24894 633 0.61970 2.940E−02 293.96476 634 0.620692.967E−02 296.70495 635 0.62167 2.995E−02 299.46973 636 0.622663.023E−02 302.25931 637 0.62365 3.051E−02 305.07393 638 0.624633.079E−02 307.91380 639 0.62562 3.108E−02 310.77915 640 0.626603.137E−02 313.67020 641 0.62759 3.166E−02 316.58719 642 0.628573.195E−02 319.53033 643 0.62956 3.225E−02 322.49987 644 0.630543.255E−02 325.49605 645 0.63153 3.285E−02 328.51909 646 0.632513.316E−02 331.56923 647 0.63350 3.346E−02 334.64673 648 0.634483.378E−02 337.75181 649 0.63547 3.409E−02 340.88473 650 0.636453.440E−02 344.04574 651 0.63744 3.472E−02 347.23569 652 0.638423.505E−02 350.45302 653 0.63941 3.537E−02 353.69979 654 0.640393.570E−02 356.97566 655 0.64138 3.603E−02 360.28090 656 0.642363.636E−02 363.61575 657 0.64335 3.670E−02 366.98049 658 0.644333.704E−02 370.37537 659 0.64532 3.738E−02 373.80068 660 0.646313.773E−02 377.25668 661 0.64729 3.807E−02 380.74365 662 0.648283.843E−02 384.26186 663 0.64926 3.878E−02 387.81159 664 0.650253.914E−02 391.39312 665 0.65123 3.950E−02 395.00674 666 0.652223.987E−02 398.65273 667 0.65320 4.023E−02 402.33138 668 0.654194.660E−02 406.04299 669 0.65517 4.098E−02 409.78784 670 0.656164.136E−02 413.56624 671 0.65714 4.174E−02 417.37849 672 0.658134.212E−02 421.22488 673 0.65911 4.251E−02 425.10573 674 0.660104.290E−02 429.02134 675 0.66108 4.330E−02 432.97202 676 0.662074.370E−02 436.95808 677 0.66305 4.410E−02 440.97986 678 0.664044.450E−02 445.03765 679 0.66502 4.491E−02 449.13179 680 0.666014.533E−02 453.26260 681 0.66700 4.574E−02 457.43041 682 0.667984.616E−02 461.63555 683 0.66897 4.659E−02 465.87835 684 0.669954.762E−02 470.15916 685 0.67094 4.745E−02 474.47831 686 0.671924.788E−02 478.83615 687 0.67291 4.832E−02 483.23302 688 0.673894.877E−02 487.66928 689 0.67488 4.921E−02 492.14528 690 0.675864.967E−02 496.66137 691 0.67685 5.012E−02 501.21792 692 0.677835.058E−02 505.81528 693 0.67882 5.105E−02 510.45383 694 0.679805.151E−02 515.13393 695 0.68079 5.199E−02 519.85596 696 0.681775.246E−02 524.62029 697 0.68276 5.294E−02 529.42731 698 0.683745.343E−02 534.27740 699 0.68473 5.392E−02 539.17694 700 0.685715.441E−02 544.10833 701 0.68670 5.491E−02 549.08996 702 0.687685.541E−02 554.11624 703 0.68867 5.592E−02 559.18755 704 0.689665.643E−02 564.30431 705 0.69064 5.695E−02 569.46692 706 0.691635.747E−02 574.67581 707 0.69261 5.799E−02 579.93138 708 0.693605.852E−02 585.23405 709 0.69458 5.906E−02 590.58426 710 0.695575.960E−02 595.98243 711 0.69655 6.014E−02 601.42899 712 0.697546.069E−02 606.92438 713 0.69852 6.125E−02 612.46904 714 0.699516.181E−02 618.06341 715 0.70049 6.237E−02 623.70795 716 0.701486.294E−02 629.40310 717 0.70246 6.351E−02 635.14933 718 0.703456.409E−02 640.94709 719 0.70443 6.468E−02 646.79685 720 0.705426.527E−02 652.69908 721 0.70640 6.587E−02 658.65426 722 0.707396.647E−02 664.66286 723 0.70837 6.707E−02 670.72537 724 0.709366.768E−02 676.84228 725 0.71034 6.830E−02 683.01407 726 0.711336.892E−02 689.24124 727 0.71232 6.955E−02 695.52430 728 0.713307.019E−02 701.86376 729 0.71429 7.083E−02 708.26011 730 0.715277.147E−02 714.71389 731 0.71626 7.212E−02 721.22561 732 0.717247.278E−02 727.79579 733 0.71823 7.344E−02 734.42496 734 0.719217.411E−02 741.11367 735 0.72020 7.479E−02 747.86245 736 0.721187.547E−02 754.67184 737 0.72217 7.615E−02 761.54240 738 0.723157.685E−02 768.47469 739 0.72414 7.755E−02 775.46925 740 0.725127.825E−02 782.52667 741 0.72611 7.896E−02 789.64751 742 0.727097.968E−02 796.83234 743 0.72808 8.041E−02 804.08176 744 0.729068.114E−02 811.39634 745 0.73005 8.188E−02 818.77668 746 0.731038.262E−02 826.22339 747 0.73202 8.337E−02 833.73706 748 0.733008.413E−02 841.31830 749 0.73399 8.490E−02 848.96773 750 0.734988.567E−02 856.68597 751 0.73596 8.645E−02 864.47366 752 0.736958.723E−02 872.33141 753 0.73793 8.803E−02 880.25988 754 0.738928.883E−02 888.25970 755 0.73990 8.963E−02 896.33154 756 0.740899.045E−02 904.47604 757 0.74187 9.127E−02 912.69387 758 0.742869.210E−02 920.98570 759 0.74384 9.294E−02 929.35220 760 0.744839.378E−02 937.79407 761 0.74581 9.463E−02 946.31199 762 0.746809.549E−02 954.90665 763 0.74778 9.636E−02 963.57876 764 0.748779.723E−02 972.32902 765 0.74975 9.812E−02 981.15816 766 0.750749.901E−02 990.06690 767 0.75172 9.991E−02 999.05595 768 0.752711.008E−01 1008.12607 769 0.75369 1.017E−01 1017.27800 770 0.754681.027E−01 1026.51247 771 0.75567 1.036E−01 1035.83626 772 0.756651.045E−01 1045.23213 773 0.75764 1.055E−01 1054.71885 774 0.758621.064E−01 1064.29119 775 0.75961 1.074E−01 1073.94996 776 0.760591.084E−01 1083.69593 777 0.76158 1.094E−01 1093.52991 778 0.762561.103E−01 1103.45271 779 0.76355 1.113E−01 1113.46516 780 0.764531.124E−01 1123.56806 781 0.76552 1.134E−01 1133.76227 782 0.766501.144E−01 1144.04861 783 0.76749 1.154E−01 1154.42793 784 0.768471.165E−01 1164.90110 785 0.76946 1.175E−01 1175.46898 786 0.770441.186E−01 1186.13245 787 0.77143 1.197E−01 1196.89237 788 0.772411.208E−01 1207.74965 789 0.77340 1.219E−01 1218.70519 790 0.774381.230E−01 1229.75989 791 0.77537 1.241E−01 1240.91466 792 0.776351.252E−01 1252.17044 793 0.77734 1.264E−01 1263.52815 794 0.778331.275E−01 1274.98874 795 0.77931 1.287E−01 1286.55317 796 0.780301.298E−01 1298.22238 797 0.78128 1.310E−01 1309.99736 798 0.782271.322E−01 1321.87908 799 0.78325 1.334E−01 1333.86853 800 0.784241.346E−01 1345.96672 801 0.78522 1.358E−01 1358.17464 802 0.786211.370E−01 1370.49332 803 0.78719 1.383E−01 1382.92378 804 0.788181.395E−01 1395.46706 805 0.78916 1.408E−01 1408.12422 806 0.790151.421E−01 1420.89630 807 0.79113 1.434E−01 1433.78438 808 0.792121.447E−01 1446.78954 809 0.79310 1.460E−01 1459.91285 810 0.794091.473E−01 1473.15543 811 0.79507 1.487E−01 1486.51839 812 0.796061.500E−01 1500.00283 813 0.79704 1.514E−01 1513.60991 814 0.798031.527E−01 1527.34075 815 0.79901 1.541E−01 1541.19651 816 0.800001.555E−01 1555.17836 817 0.80099 1.569E−01 1569.28748 818 0.801971.584E−01 1583.52505 819 0.80296 1.598E−01 1597.89226 820 0.803941.612E−01 1612.39034 821 0.80493 1.627E−01 1627.02051 822 0.805911.642E−01 1641.78399 823 0.80690 1.657E−01 1656.68205 824 0.807881.672E−01 1671.71592 825 0.80887 1.687E−01 1686.88689 826 0.809851.702E−01 1702.19625 827 0.81084 1.718E−01 1717.64528 828 0.811821.733E−01 1733.23529 829 0.81281 1.749E−01 1748.96761 830 0.813791.765E−01 1764.84357 831 0.81478 1.781E−01 1780.86453 832 0.815761.797E−01 1797.03183 833 0.81675 1.813E−01 1813.34685 834 0.817731.830E−01 1829.81099 835 0.81872 1.846E−01 1846.42564 836 0.819701.863E−01 1863.19222 837 0.82069 1.880E−01 1880.11216 838 0.821671.897E−01 1897.18689 839 0.82266 1.914E−01 1914.41788 840 0.823651.932E−01 1931.80660 841 0.82463 1.949E−01 1949.35454 842 0.825621.967E−01 1967.06319 843 0.82660 1.985E−01 1984.93407 844 0.827592.003E−01 2002.96871 845 0.82857 2.021E−01 2021.16866 846 0.829562.040E−01 2039.53547 847 0.83054 2.058E−01 2058.07072 848 0.831532.077E−01 2076.77601 849 0.83251 2.096E−01 2095.65294 850 0.833502.115E−01 2114.70314 851 0.83448 2.134E−01 2133.92824 852 0.835472.153E−01 2153.32990 853 0.83645 2.173E−01 2172.90979 854 0.837442.193E−01 2192.66960 855 0.83842 2.213E−01 2212.61104 856 0.839412.233E−01 2232.73582 857 0.84039 2.253E−01 2253.04569 858 0.841382.274E−01 2273.54240 859 0.84236 2.294E−01 2294.22773 860 0.843352.315E−01 2315.10346 861 0.84433 2.336E−01 2336.17142 862 0.845322.357E−01 2357.43342 863 0.84631 2.379E−01 2378.89131 864 0.847292.401E−01 2400.54696 865 0.84828 2.422E−01 2422.40224 866 0.849262.444E−01 2444.45906 867 0.85025 2.467E−01 2466.71934 868 0.851232.489E−01 2489.18502 869 0.85222 2.512E−01 2511.85806 870 0.853202.535E−01 2534.74043 871 0.85419 2.558E−01 2557.83414 872 0.855172.581E−01 2581.14120 873 0.85616 2.605E−01 2604.66365 874 0.857142.628E−01 2628.40356 875 0.85813 2.652E−01 2652.36299 876 0.859112.677E−01 2676.54405 877 0.86010 2.701E−01 2700.94886 878 0.861082.726E−01 2725.57957 879 0.86207 2.750E−01 2750.43834 880 0.863052.776E−01 2775.52735 881 0.86404 2.801E−01 2800.84881 882 0.865022.826E−01 2826.40496 883 0.86601 2.852E−01 2852.19805 884 0.867002.878E−01 2878.23034 885 0.86798 2.905E−01 2904.50415 886 0.868972.931E−01 2931.02179 887 0.86995 2.958E−01 2957.78560 888 0.870942.985E−01 2984.79796 889 0.87192 3.012E−01 3012.06126 890 0.872913.040E−01 3039.57792 891 0.87389 3.067E−01 3067.35037 892 0.874883.095E−01 3095.38108 893 0.87586 3.124E−01 3123.67255 894 0.876853.152E−01 3152.22729 895 0.87783 3.181E−01 3181.04784 896 0.878823.210E−01 3210.13677 897 0.87980 3.239E−01 3239.49668 898 0.880793.269E−01 3269.13018 899 0.88177 3.299E−01 3299.03992 900 0.882763.329E−01 3329.22857 901 0.88374 3.360E−01 3359.69884 902 0.884733.390E−01 3390.45346 903 0.88571 3.421E−01 3421.49517 904 0.886703.453E−01 3452.82676 905 0.88768 3.484E−01 3484.45106 906 0.888673.516E−01 3516.37089 907 0.88966 3.549E−01 3548.58913 908 0.890643.581E−01 3581.10868 909 0.89163 3.614E−01 3613.93247 910 0.892613.647E−01 3647.06346 911 0.89360 3.681E−01 3680.50463 912 0.894583.714E−01 3714.25901 913 0.89557 3.748E−01 3748.32965 914 0.896553.783E−01 3782.71964 915 0.89754 3.817E−01 3817.43208 916 0.898523.852E−01 3852.47012 917 0.89951 3.888E−01 3887.83695 918 0.900493.924E−01 3923.53576 919 0.90148 3.960E−01 3959.56982 920 0.902463.996E−01 3995.94239 921 0.90345 4.033E−01 4032.65679 922 0.904434.070E−01 4069.71636 923 0.90542 4.107E−01 4107.12448 924 0.906404.145E−01 4144.88457 925 0.90739 4.183E−01 4183.00009 926 0.908374.221E−01 4221.47450 927 0.90936 4.260E−01 4260.31135 928 0.910344.300E−01 4299.51418 929 0.91133 4.339E−01 4339.08659 930 0.912324.379E−01 4379.63221 931 0.91330 4.419E−01 4419.35473 932 0.914294.460E−01 4460.05783 933 0.91527 4.501E−01 4501.14528 934 0.916264.543E−01 4542.62085 935 0.91724 4.584E−01 4584.48837 936 0.918234.627E−01 4626.75172 937 0.91921 4.669E−01 4669.41478 938 0.920204.712E−01 4712.48152 939 0.92118 4.756E−01 4755.95591 940 0.922174.800E−01 4799.84198 941 0.92315 4.844E−01 4844.14381 942 0.924144.889E−01 4888.86551 943 0.92512 4.934E−01 4934.01124 944 0.926114.980E−01 4979.58519 945 0.92709 5.026E−01 5025.59161 946 0.928085.072E−01 5072.03478 947 0.92906 5.119E−01 5118.91905 948 0.930055.166E−01 5166.24879 949 0.93103 5.214E−01 5214.02842 950 0.932025.262E−01 5262.26241 951 0.93300 5.311E−01 5310.95529 952 0.933995.360E−01 5360.11161 953 0.93498 5.410E−01 5409.73600 954 0.935965.460E−01 5459.83311 955 0.93695 5.510E−01 5510.40765 956 0.937935.561E−01 5561.46439 957 0.93892 5.613E−01 5613.00814 958 0.939905.665E−01 5665.04375 959 0.94089 5.718E−01 5717.57614 960 0.941875.771E−01 5770.61028 961 0.94286 5.824E−01 5824.15118 962 0.943845.878E−01 5878.20392 963 0.94483 5.933E−01 5932.77361 964 0.945815.988E−01 5987.86545 965 0.94680 6.043E−01 6043.48465 966 0.947786.100E−01 6099.63651 967 0.94877 6.156E−01 6156.32637 968 0.949756.214E−01 6213.55964 969 0.95074 6.271E−01 6271.34178 970 0.951726.330E−01 6329.67830 971 0.95271 6.389E−01 6388.57478 972 0.953696.448E−01 6448.03685 973 0.95468 6.508E−01 6508.07022 974 0.955676.569E−01 6568.68063 975 0.95665 6.630E−01 6629.87391 976 0.957646.692E−01 6691.65593 977 0.95862 6.754E−01 6754.03264 978 0.959616.817E−01 6817.01005 979 0.96059 6.881E−01 6886.59422 980 0.961586.945E−01 6944.79129 981 0.96256 7.010E−01 7009.60746 982 0.963557.075E−01 7075.04901 983 0.96453 7.141E−01 7141.12226 984 0.965527.208E−01 7207.83362 985 0.96650 7.275E−01 7275.18956 986 0.967497.343E−01 7343.19663 987 0.96847 7.412E−01 7411.86143 988 0.969467.481E−01 7481.19065 989 0.97044 7.551E−01 7551.19105 990 0.971437.622E−01 7621.86945 991 0.97241 7.693E−01 7693.23276 992 0.973407.765E−01 7765.28795 993 0.97438 7.838E−01 7838.04207 994 0.975377.912E−01 7911.50226 995 0.97635 7.986E−01 7985.67571 996 0.977348.061E−01 8060.56972 997 0.97833 8.136E−01 8136.19165 998 0.979318.213E−01 8212.54893 999 0.98030 8.290E−01 8289.64909 1000 0.981288.367E−01 8367.49974 1001 0.98227 8.446E−01 8446.10856 1002 0.983258.525E−01 8525.48333 1003 0.98424 8.606E−01 8605.63189 1004 0.985228.687E−01 8686.56220 1005 0.98621 8.768E−01 8768.28228 1006 0.987198.851E−01 8850.80025 1007 0.98818 8.934E−01 8934.12431 1008 0.989169.018E−01 9018.26275 1009 0.99015 9.103E−01 9103.22396 1010 0.991139.189E−01 9189.01642 1011 0.99212 9.276E−01 9275.64869 1012 0.993109.363E−01 9363.12944 1013 0.99409 9.451E−01 9451.46742 1014 0.995079.541E−01 9540.67150 1015 0.99606 9.631E−01 9630.75061 1016 0.997049.722E−01 9721.71382 1017 0.99803 9.814E−01 9813.57027 1018 0.999019.906E−01 9906.32922 1019 1.00000 1.000E+00 10000.00000 1020 Reserved1021 Reserved 1022 Reserved 1023 Reserved

In the foregoing specification, embodiments of the invention have beendescribed with reference to numerous specific details that may vary fromimplementation to implementation. Thus, the sole and exclusive indicatorof what is the invention, and is intended by the applicants to be theinvention, is the set of claims that issue from this application, in thespecific form in which such claims issue, including any subsequentcorrection. Any definitions expressly set forth herein for termscontained in such claims shall govern the meaning of such terms as usedin the claims. Hence, no limitation, element, property, feature,advantage or attribute that is not expressly recited in a claim shouldlimit the scope of such claim in any way. The specification and drawingsare, accordingly, to be regarded in an illustrative rather than arestrictive sense.

The invention claimed is:
 1. A method performed on an imaging device fortranscoding reference encoded image data into device-specific imagedata, the method comprising the steps of: determining a digital codemapping between a set of reference digital code values and a set ofdevice-specific digital code values, wherein the set of referencedigital code values is mapped in a reference mapping to a set ofreference gray levels, and wherein the set of device-specific digitalcode values is mapped in a device-specific mapping to a set ofdevice-specific gray levels; receiving reference encoded image dataencoded with the set of reference digital code values, wherein luminancevalues in the reference encoded image data are based on the set ofreference digital code values, wherein a luminance difference betweentwo reference gray levels represented by two adjacent reference digitalcode values in the set of reference digital code values is inverselyproportional to a peak contrast sensitivity of human vision adapted at aparticular light level; and transcoding, based on the digital codemapping, the reference encoded image data encoded with the set ofreference digital code values into device-specific image data encodedwith the set of device-specific digital control codes, wherein luminancevalues in the device-specific image data are based on the set ofdevice-specific digital code values; wherein at least one of thereference mapping and the device-specific mapping is determined based atleast in part on a functional model represented with the function$L = \left\lbrack \frac{D^{1/m} - c_{1}}{c_{2} - {c_{3}D^{1/m}}} \right\rbrack^{1/n}$wherein D represents a digital code value to be mapped, and L representsa gray level corresponding to the digital code value.
 2. The method asrecited in claim 1, further comprising: determining a set ofcorrespondence relationships between the set of reference digital codevalues and the set of device-specific digital code values, wherein acorrespondence relationship in the set of correspondence relationshiprelates a reference digital code value in the set of reference digitalcode values to a device-specific digital code value; comparing a firstluminance difference at the reference digital code value and a secondluminance difference at the device-specific digital code value; storing,based on comparing the first luminance difference and the secondluminance difference, an algorithm flag as to whether dithering,decontouring, or no operation should be performed for the referencedigital code value; determining the reference digital code value fromthe reference encoded image data for a pixel; determining whether thealgorithm flag is set for the reference digital code value; and inresponse to determining that an algorithm flag is set for decontour,performing a decontour algorithm on the pixel, or, in response todetermining that an algorithm flag is set for dithering, performing adithering algorithm on the pixel.
 3. The method as recited in claim 1,further comprising rendering one or more images on a display based onthe device-specific image data encoded with the set of device-specificdigital control codes, the display being one of a visible dynamic range(VDR) display, a low dynamic range (LDR) display, a tablet computerdisplay, or a handheld device display.
 4. The method as recited in claim1, wherein a device-specific gray scale display function (GSDF)specifies the device-specific mapping between the set of device-specificdigital code values and the set of device-specific gray levels.
 5. Themethod as recited in claim 1, wherein the device-specific mapping isderived based on one or more display parameters and zero or more viewingcondition parameters.
 6. The method as recited in claim 1, wherein theset of device-specific gray levels covers a dynamic range with an upperlimit having a value of: less than 100 nits; no less than 100 nits butless than 500 nits; between 500 nits and 1000 nits, inclusive; between1000 and 5000 nits, inclusive; between 5000 nits and 10000 nits,inclusive; or greater than 10000 nits.
 7. The method as recited in claim1, further comprising converting one or more input images represented,received, transmitted, or stored with the reference encoded image datafrom an input video signal into one or more output images represented,received, transmitted, or stored with the device-specific image datacontained in an output video signal.
 8. The method as recited in claim1, wherein the device-specific image data supports image rendering inone of a high-resolution high dynamic range (HDR) image format, a RGBcolor space associated with the Academy Color Encoding Specification(ACES) standard of the Academy of Motion Picture Arts and Sciences(AMPAS), a P3 color space standard of the Digital Cinema Initiative, aReference Input Medium Metric/Reference Output Medium Metric (RIMM/ROMM)standard, an sRGB color space, or a RGB color space associated with theBT.709 Recommendation standard of the International TelecommunicationsUnion (ITU).
 9. The method as recited in claim 1, wherein the luminancedifference between the two reference gray levels represented by the twoadjacent reference digital code values is less than a just noticeabledifference threshold at the particular light level.
 10. The method asrecited in claim 1, wherein the particular light level comprises aluminance value between the two luminance values, inclusive.
 11. Themethod as recited in claim 1, wherein the set of device-specific digitalcode values comprises integer values in a code space with a bit depthof: 8 bits; greater than 8 but less than 12 bits; or 12 bits or more.12. The method as recited in claim 1, wherein the set of device-specificgray levels comprises a set of quantized luminance values.
 13. Themethod as recited in claim 1, wherein values of the model parameters n,m, c₁, c₂ and c₃ are optimized through minimizing deviations betweenpredicted code values and target code values.
 14. The method as recitedin claim 1, wherein the reference digital code values and thedevice-specific digital code values are quantized in quantization steps,and wherein a first quantization step size relates to a peak contrastsensitivity of human vision adapted to a first light level to spatialfrequency.
 15. The method as recited in claim 14, wherein the firstquantization step size is less than a just noticeable differencethreshold at the first light level.
 16. The method as recited in claim14, wherein a second quantization step size relates to a peak contrastsensitivity of human vision adapted at a second light level to spatialfrequency, the first and second quantization step sizes differ.
 17. Themethod as recited in claim 16, wherein the first light level is lessthan the second light level, and the first quantization step size islarger than the second quantization step size.
 18. An imaging device,configured to display device-specific image data, performing a methodcomprising the steps of: determining a digital code mapping between aset of reference digital code values and a set of device-specificdigital code values, wherein the set of reference digital code values ismapped in a reference mapping to a set of reference gray levels, andwherein the set of device-specific digital code values is mapped in adevice-specific mapping to a set of device-specific gray levels;receiving reference encoded image data encoded with the set of referencedigital code values, wherein luminance values in the reference encodedimage data are based on the set of reference digital code values,wherein a luminance difference between two reference gray levelsrepresented by two adjacent reference digital code values in the set ofreference digital code values is inversely proportional to a peakcontrast sensitivity of human vision adapted at a particular lightlevel; and transcoding, based on the digital code mapping, the referenceencoded image data encoded with the set of reference digital code valuesinto device-specific image data encoded with the set of device-specificdigital control codes, wherein luminance values in the device-specificimage data are based on the set of device-specific digital code values;wherein at least one of the reference mapping and the device-specificmapping is determined based at least in part on a functional modelrepresented with the function$L = \left\lbrack \frac{D^{1/m} - c_{1}}{c_{2} - {c_{3}D^{1/m}}} \right\rbrack^{1/n}$wherein D represents a digital code value to be mapped, and L representsa gray level corresponding to the digital code value.
 19. The imagingdevice as recited in claim 18, wherein the imaging device comprises alow dynamic range display.
 20. The imaging device as recited in claim18, wherein the imaging device is configured to support a field of viewof one of an intermediate horizontal angular size between 40 degrees and25 degrees, and a narrow horizontal angular size no more than 25degrees.
 21. The imaging device as recited in claim 18, wherein theimaging device is configured to support one of an intermediate viewingdistance between 1.5 meter and 0.5 meter, and a short viewing distanceof no more than 0.5 meter.
 22. Storage or transmission, non-transitorymedia storing instructions which, when executed, cause one or moreprocessors to perform a method comprising the steps of: determining adigital code mapping between a set of reference digital code values anda set of device-specific digital code values, wherein the set ofreference digital code values is mapped in a reference mapping to a setof reference gray levels, and wherein the set of device-specific digitalcode values is mapped in a device-specific mapping to a set ofdevice-specific gray levels; receiving reference encoded image dataencoded with the set of reference digital code values, wherein luminancevalues in the reference encoded image data are based on the set ofreference digital code values, wherein a luminance difference betweentwo reference gray levels represented by two adjacent reference digitalcode values in the set of reference digital code values is inverselyproportional to a peak contrast sensitivity of human vision adapted at aparticular light level; and transcoding, based on the digital codemapping, the reference encoded image data encoded with the set ofreference digital code values into device-specific image data encodedwith the set of device-specific digital control codes, wherein luminancevalues in the device-specific image data are based on the set ofdevice-specific digital code values; wherein at least one of thereference mapping and the device-specific mapping is determined based atleast in part on a functional model represented with the function$L = \left\lbrack \frac{D^{1/m} - c_{1}}{c_{2} - {c_{3}D^{1/m}}} \right\rbrack^{1/n}$wherein D represents a digital code value to be mapped, and L representsa gray level corresponding to the digital code value.